Cosplay isn't so much a general thing to learn as it is a large collection of crafting skills brought together by where you pick up the stuff you're working with, whether it's Home Depot, Michael's, or Jo-Ann's. :V
Learning to sew begins with the machine itself. Some places offer classes, but it's typically easier to learn from a friend/relative since a sewing machine is easy to use once you've familiarized yourself with one. Next, learn how to use a pattern, which details how exactly a garment is put together. Look to Simplicity (especially for costume stuff), McCall's & Butterick, Burda, and other companies for one. The easiest type of garment to learn how to make is probably a skirt or cape, and for a first go, any cheap fabric will do since it isn't meant to be functional. Finally, learn the ins and outs of different fabric types to figure out which fabrics to use (i.e. knit fabrics stretch and should probably only be used for garments that do, some fabrics have a grain and need to be cut a certain way, twill takes a stitch like a champ but shouldn't be used for lighter clothes, etc.). There's a lot to know and a lot to learn. If you're a bit lost, look to the pattern, which will typically provide you with a list of recommended fabric types. Once you reach a certain level of experience with making garments, you'll be able to break an outfit down into which patterns to use and how they need to be modified as well as which fabrics to use. Also, wash all fresh fabric alone so that the extra dye doesn't wind up on anything else, and the only way to ruin fabric is to cut it TOO MUCH or paint/dye it too hard. Fabric is easy to fix unless you're careless.
Arts and crafts are always different because the technique depends exclusively on what's being made. Luckily, guides for making different things are plentiful and can typically be found all over the place. Really, part of the secret is looking up what someone else did and applying it to what you're doing. Craft foam armor looks like it'll help a lot here. It's versatile, forgiving, and cheap and easy to make. A single sheet of foam costs less than a buck and the best fabric for it is less than 3 bucks a yard at worst. If you can't find some in the size you're looking for, L200 sheets are available elsewhere, but are more expensive.
It's all well and good to be experienced with woodworking because props are great. I have also started to worship medium density fiberboard and wood putty. A decent wood shop and a nice set of tools is invaluable when coupled with the right imagination and know-how.
