According to Wikipedia, Amigurumi is "the Japanese art of knitting or crocheting small stuffed animals and anthropomorphic creatures. The word is derived from a combination of the Japanese words ami, meaning crocheted or knitted, and nuigurumi, meaning stuffed doll. Amigurumi are typically animals, but can include artistic renderings, and inanimate objects endowed with anthropomorphic features.
I am really in love with these. They're so easy to make. They take about a day, depending on the size of the project or the difficulty. They make personal, cute gifts.
They all have similar starts to them. One popular one is the magic ring, or magic circle. This basically means crocheting the first stitches into a circle that you can pull tightly closed via a drawstring apparatus. YouTube is a big help in learning to do crochet stitches. The video I learned the magic circle is located here. It's one of the clearer ones.
Another option is to chain 2, and then put the desired amount of stitches in the second chain from the hook. This option works perfectly fine, it just doesn't get as tightly closed. A lot of patterns will have this as the starting option, but using the magic ring usually works well with the pattern. This is also true of patterns beginning with the magic ring/circle. You're probably fine using the chain 2 option.
If enough interest is generated, I may start a photobucket account full of how-to pictures, and link the albums on the side with the rest of the links. Leave comments and let me know. You are also perfectly welcome to email me at email@example.com and I will be happy to talk you through patterns I post here as much as I can. I'm also planning on doing giveaways of crocheted things. The first will probably be around my birthday in the coming week so keep an eye out. :D