So I recently decided to (re) learn how to crochet and knit. My mother is an avid knitter, so I initially thought I would start with that, but then turned to crocheting first as it is so much simpler! I'm now doing both, with moderate success.
Side note: Many people seem surprised that knitting and crocheting are two different things. See my easy reference above.
I had completely forgotten how to crochet (I last did so in high school), but taught myself with the help of lots of online tools. I pretty much just YouTubed my way through every stitch I encountered and was able to produce a pretty respectable stuffed animal. I found videos by "ExpertVillage" especially helpful; here is a good one to get you started. If you plan on making stuffed animals (or hats), you'll probably need to crochet in the round; here is a great website explaining an easy way to start circular rows.
I bought this amigurumi pattern on Etsy.com from LuvlyGurumi. All the patterns/products she sells are beyond adorable - check out the little bee! Amigurumi is the Japanese style of knitting/crocheting little animals; aka it results in the cutest things you have ever seen made of yarn.
I picked up all of my supplies at The Windsor Button, located near Downtown Crossing in Boston. In addition to an ungodly amount of buttons, they have a nice selection of yarn, ribbon, trimmings, and general craft supplies (which can be hard to find in Boston without venturing to the suburbs). For three skeins of (cheap acrylic) yarn, two crochet hooks, two tapestry needles, a pack of "safety eyes," and a big bag of fiberfill, I think I spent around $22.
Stuffed animals are a great craft project and gift because a) they're not season-specific and b) all ages seem to love them. So if you're searching for nice handmade Christmas gifts, you have a good three months to learn amigurumi.