There are several ways to start off an amigurumi. The method I use most is to make a slip knot, chain 2, then make the required number of stitches into the second chain from the hook. Some people don't like this technique as it can leave a hole in the centre of the first round. I find that if you crochet over the end (or rather, the 'beginning') of the yarn as you make the first round, you can then give the yarn end a firm tug to close up any hole (when I say firm, I mean firm, so don't try this with yarn that is liable to snap!).
Another technique to try is the 'magic ring' - there is a nice tutorial on this over at PlanetJune. This uses the same idea of crocheting over the yarn tail and then pulling the hole closed. No matter how many times I've tried (and I've looked at many written and video tutorials) I still end up reverting to the good old chain 2 method as I just can't get on with the magic ring...
A third method is the 'sloppy slip knot' - tutorial can be found on Fresh Stitches. I've tried it and it works, and it's easier (to me) than the magic ring.
Most designers write their patterns using the technique they prefer, but you can, of course, use whichever method suits you best.