Depending upon where you live, zoning laws may prevent you from having a nice, sustainable backyard barnyard. Do check your zoning laws because you may be pleasantly surprised about what you can and cannot have in your suburb, exurb, or city backyard.
Where I live, I can have a mini cow that doesn't exceed 38" in height so long as I have it as a pet and for milk, not for slaughter. I can have chickens for eggs, but not for slaughter. I can raise rabbits for "wool", fur, and meat. I cannot have goats regardless of size, nor horses, or pigs. I couldn't find anything about having a fish pond and stocking it so I will operate on the assumption that what is not banned is allowed.
This is just a brief overview of what you might face if you choose to have a backyard barnyard of your own, from just a chicken or two to a full yard of cows, goats, chickens, bunnies, and ducks. I hope other members with their personal experience, and/or from other parts of the country, will contribute diaries about their experiences with backyard barnyards, particularly if they live in the suburbs or cities.
Fish ponds are for another diary.
Still, I can - in my small suburban plot of land, have a tiny milch cow, a few chickens, and some rabbits for "wool", fur, and meat - and possibly raise fish to eat.
I can grow rice, wheat, potatoes, spinach, tomatoes, herbs, onions, garlic, rutabagas, celery, cabbages, cauliflower, carrots, lettuces, sunflowers, pecans, acorns, apples, redbuds, dandelions, raspberries, strawberries, blueberries, broccoli, Brussels sprouts, sweet peas, snow peas, summer squashes, winter squashes, and edible flowers in front and back where the cow isn't grazing, and the chickens can spend time in the garden eating bugs. The bunnies will have to be in a run and I'm not sure at this point I want to deal with bunnies.
But - acowand chickens. I grew up with cows and chickens and I know how to care for them. I have to wait until my son takes his big dogs back when he gets out of the army, and when he does - I'm going to find me a nice tiny cow - a Dexter would be nice, but a Santa Isabel cow that's only 25" tall would be very good. I'll likely be getting a Holstein or a Jersey, though as those seem easier to find locally.
If you want to check into having your own backyard barnyard, your first place is to check your local zoning laws. The assumption is that if it's not forbidden, it's legal. You may still have to address your HOA or local zoning board, and arming yourself with facts is the best way to go.
Your next step is to determine if your plot of land is large enough to responsibly raise the type and number of backyard barnyard critters you want. If you don't have enough land, it ends here unless you sell and move where there is enough land space. and the zoning check starts all over again - easier because you can check the zoning before you buy the land.
If you rent, you will have to get the permission of your landlord.
Once you have the land size and zoning in order, your next step is to win over your neighbors.
Talk to your neighbors and let them know what you plan to do. Make sure they are OK with it because the quickest way to get fined and in trouble with your local neighborhood association and city zoning commission is to have neighbors complain. If you present it as a pet, and let them get to know the animal, neighbors will be less likely to complain. Leash train your cow and take it for walks in the neighborhood just as you would a dog - if the kids in the neighborhood love your cow, their parents are likely to also be happy with your cow. If you keep the poop scooped and deodorized (composting it is ideal unless you live in a city or neighborhood that forbids composting, in which case you can take it to someone who can compost - consider bartering - you get my cow's manure and I get X pounds of organic compost back), your neighbors will have less to complain about.
An ordinary tool shed will work as a barn for your mini cow. Have it wired for heat and cooling, put in a stall where you can comfortably milk your little cow, have a place to store extra hay and feed, and put in a good floor you can clean well. If your shed is large enough, you can keep your garden tools in there, hay for the little cow, and even put in a small roost for your chickens. Chickens and cows are good companions.
Check out some good books about raising small barnyard animals, like Barnyard in your Backyard by Gail Damerow, or Mini Farming for Self Sufficiency by Brett Markham.
Talk to local farmers about problems. Get on the good side of your neighbors. If you can convince a few neighbors to also do some mini farming in their backyards, you'll have a support group to help you when some other neighbor complains.
There are a variety of good websites to check, too, like Urban Chickens, Mad City Chickens, Backyard Chickens, Backyard Cows, and Backyard Farmer.
Once you have the support of your neighbors, and have done research on the types of livestock your city allows, and know how much land you have available, you'll probably want to choose the type of livestock you want to have. Mini cows, goats, chickens, rabbits, ducks, geese, and pigs are all possibilities, perhaps even sheep. You'll be limited by the amount of land you have. Suburban lots tend to be between 1/8 and 1/3 of an acre, so a few ducks, chickens, or rabbits and possibly a nanny goat or a very small mini cow would be happy there. The bigger the house, the less land you generally have. In an inner city or apartment or condo, you'll have even less space. Chickens, ducks, and rabbits are a possibility in apartment or condo living situations.
After you've chosen the type of livestock you want or can have, your next step is to prepare your yard for the livestock you'll be bringing home. Fencing, a method to take care of the droppings, a place to keep your new livestock in comfort, a way to deal with the eggs, milk, and other products your livestock will produce, and a first aid kit and a vet who can care for your livestock are among the things you should have in place before you bring your livestock to their new home.
When everything is in place, you've made peace with your neighbors over the livestock you've chosen, your zoning laws are happy with your choices, you have enough room, have your coops/stalls/barns built, and feed and hay and straw laid in, a vet chosen, it's time to visit farms and pick your livestock.
Since this animal (or animals) will be more than livestock (it will probably also become a pet) be sure you really like the animal. Animals do have personalities, and if you don't like the critter, do yourself and it a big favor and pick a different animal. This is going to be a commitment - a long term one. Chickens can live for years if you get them for egg laying. Rabbits also have a lifespan of 5-8 years. Goats and cows live even longer.
One thing you'll have to consider if you get a cow or goat is refreshing them. To refresh their milk, they will have to be impregnated now and then. You can probably get them artificially inseminated through your vet or from the farmer from whom you bought your cow or goat. When your cow or goat is impregnated to refresh their milk, there will be babies. You can raise the baby if you want, but you'll be sharing your milk with the baby. You can take it to the farmer to be slaughtered, or, if it's female, you can sell it to someone else who wants a cow or goat. You can also handraise the baby and bottle feed it so you still get the milk your cow or goat produces. Bulls and billygoats are best slaughtered, something you can arrange through the farmer from whom you bought your cow or goat.
Goats are curious and they can and will get into everything. They are like the toddler that puts everything in its mouth, except they will then also eat it. Goats will eat your laundry right off the line, will eat the cables and wires leading to your house, they'll eat everything in your garden. They will eat your wooden stockade fence and those newer vinyl fences. They will gnaw on wooden posts. They jump, too, so a tall fence is needed, possibly even one with a roof over it, like a chicken coop, but goat-sized. Goats need to be strongly confined away from anything they can destroy by biting, chewing, nibbling, or eating it. On the plus side, nanny goats are cuddly, give good milk, and walk well on a leash. Billy goats - don't even go there. For a small backyard barnyard, pygmy nanny goats are pretty much the way to go.
Cows are much more placid than goats. They are just as curious, but far less destructive. They won't chew your cables, fences, or laundry, but they will eat much of your garden if you let them. Cows will often act like a dog, and will want to follow you indoors. They like attention and appreciate being groomed, milked, talked to. They will walk well on a leash, but they are plodding walkers. If you want to jog, walk a goat or a dog. If you like a leisurely walk, walk a cow.
With both cows and goats, you will have odor problems. Nanny goats and milk cows smell much better than bulls or billy goats, but they still poop. Poop needs to be dealt with quickly. They can be taught to poop in one place, but it takes a lot of dedicated attention to potty train them. A lot. It's much easier to control their feed so they have regular bowel movements and scoop their poop as quickly as you can. Put it in a container if you're taking it to someone else to compost, or dig it immediately into the compost if you have a compost. Keep their barn clean, scrub it daily to reduce flies. You won't be able to get rid of the flies entirely, but you can keep them down to reasonable levels with fly strips and frequent cleaning.
Bathe your cow or goat. They will appreciate it and so will your neighbors. It will help reduce the smell and the flies, too.
Chicken droppings are harder to control. I've heard the Deep Litter Method works well. Once or twice a year, you can scrape it all out for compost and start over. I would have to try it before I could say anything. When I was growing up, our chickens were free range, if you consider the fact that they were kept in a courtyard that was surrounded on all four sides by houses with no gap between the houses. We'd "sweep" the courtyard every morning and pile the sweepings in a wheelbarrow that we'd cart over to the compost. Where we grew flowers and such, we'd dig up the earth a bit with hand rakes to smoosh droppings into the soil. We didn't have a big problem with flies or garden pests, but sometimes, especially in summer, there'd be a smell. It wasn't bad, not considering the pigs lived across the street and they truly did smell.
Even in the city, there are predators for chickens, so a strong, fully enclosed coop is best for them. Cats, dogs, hawks, raccoons, coyotes, foxes, and skunks all eat chickens, and I've seen all of these in my suburban neighborhood. In fact, I lost a trash can to a vixen denning in it. I let her keep the trash can and she's denned in it for several years with babies. They live and hunt in the park across the street. If I get chickens, I will have to reconsider our relationship and possibly move the trash can to some other location we can both be happy with. A sturdy coop with at least 5 square feet per chicken and a locking door will help keep the predators out and the chickens in and happy. You can let the chickens out of the coop when you are present to watch for predators, but be sure to keep their wings clipped - chicken can and will fly, especially if startled or chased.
Unless you're keeping a pig for meat, there really is no reason to raise pigs in your backyard. Ditto for sheep. Both need more space than the average backyard offers and they both smell more than most neighbors will tolerate. Chickens, muscovy ducks, rabbits, cows, and nanny goats can be kept comparatively quiet and clean and the odor under control. but pigs - no matter how well fed and cared for and clean they are, their poop is just awful. They also tend to be noisier than other barnyard livestock.
Sheep are noisy, smelly, and need to graze far more land than the average backyard provides. They like to roam a lot, too. Their poop is not as bad as pig poop, but it's not exactly perfume, either. Wet wool reeks, and the sheep in full wool are smelly. You'll either need to learn to shear your sheep or hire someone to shear it and by spring (when sheep are usually sheared so their wool grows back over the summer and winter), the sheep will smell pretty strongly. If you've got the land and the neighbors are good with it, sheep provide good wool, lanolin, and tasty meat. They need to be watched carefully, though, because sheep are pretty oblivious to the world around them. They'll get into trouble in a heartbeat. A sturdy fence will help.
Geese are not recommended for city backyards - they are large, loud, and smelly. I love geese. I grew up as a goosegirl, taking care of a flock of geese, and they were loyal birds. I collected their down and feathers and eggs. But they were loud, honking and calling all the time. They could be very aggressive. Their poop is particularly strong and icky.
Rabbits are useful animals to raise - they provide "wool" that can be spun into yarn, they provide skin and fur that can be made into blankets, jackets, earmuffs, gloves, vests, and trim for dress gowns and coats, they provide good meat to eat, and they provide a good manure. Like chickens, they need to be kept in a cage or hutch of their own to protect them from the same predators that love chickens. Unlike chickens, their hutch shouldn't be wood because they will gnaw on it. Instead, build them a metal hutch slightly off the ground (so they don't burrow) and give them plenty of good things to gnaw on - carrots, the inner core of cabbages, elm or apple branches, and such. Even giving the rabbits kitchen scraps doesn't reduce the overall expense of raising the rabbit solely for meat. It's usually cheaper to buy rabbits from the grocer than to raise a few just for meat. Most rabbits don't have a lot of meat on them anyway. If you raise rabbits, consider raising them for their "wool" and manure.
Since rabbits and chickens share some diseases, it's best not to raise them too close together. If your yard is small, choose just one.
Food security is so important that taking the time to at least consider raising your own livestock is important. Even if you decide you don't want to raise livestock that will provide you with milk or eggs, knowing about them and how they should be cared for will help you if a neighbor chooses to raise their own livestock near you.