I'm going to presuppose, for this post, that you already have fabric. All the gods know we have a surplus of all kinds of fabric in this society, as if we were afraid we'd end up cold and naked at any moment.
With fabric, scissors (or a knife), a needle, and thread (which you can get from fabric), you can fashion a lot of survival gear. If you're wise, you've stocked up on lots and lots of sewing needles in different sizes and straight pins and T-pins and safety pins. If not, you can make these out of bone, but that's a subject for another post. Here and now, we're discussing basic sewing.
First thing you need to do is master threading the needle. If you have vision problems, invest in a number of needle threaders. I prefer the thin wire ones because you can thread any size needle with one.
The basics you'll need to know for sewing once you've mastered threading the needle are hemming anything from pants and skirts to sheets and blankets, sewing on a button, fixing and sewing a buttonhole, darning socks, and joining two pieces of fabric together.
Once you can do those, you'll want to know about making them functional and good looking. For that you will need to learn how to place a pattern on your fabric, how to pin it in place, how to mark and cut a pattern, and how to sew it together. This last video shows you how to do it with a machine, but anything you can do with a machine, you can also do by hand in a situation where you must sew something together and have no power. If you have power, by all means, use a sewing machine. If you can generate power to fuel a sewing machine, it's faster, easier, and often sturdier than hand sewing.
But sewing by machine is a whole different set of skills. Each machine is threaded slightly differently, requires tuning and care, and has its own set of stitches it will do. Read the manual that comes with the machine if you buy one. Sewing machines are very cheap right now. I love the Pixie Plus mini sewing machine for simple, basic sewing. It only has 2 stitches: straight and zigzag, in 3 sizes. It doesn't do buttonholes. I bought mine for $39 and Amazon has it for $45.88. For a simple, basic machine, this one is a good one. If you want a machine that does buttonholes, this basic Janome can often be found on sale in fabric stores for around $80, or for $149.00 on Amazon.
You can also learn to sew using a treadle machine. This site links to many other articles on repairing and using treadle machines, mostly Singers. These machines are easy to care for and right now, are cheap and easy enough to find at places like flea markets and estate sales. I have 2 treadle machines, one my son gave me that he found discarded by the side of the road. The other one has been in my family since it was brand spanking new, and will likely pass down to my children and grandchildren, still sewing, still useful.
There's a whole lot more to learn about sewing, but these are the absolute basics - threading a needle, basic stitching, darning, hemming, and buttonholes.
I recommend locating your local fabric and sewing machine store and taking a class or two in sewing. Quilting stores will also offer sewing classes, and quilting is a useful skill for using up small scraps of fabric. The techniques you can learn for quilting translate well into the techniques for sewing clothing, tents, covers, tarps, bags, and pocket storage containers.