How to Fasten Off
Fastening off is the step that locks your crochet in place so it won't come undone once you're finished. You'll usually do it at the end of a project, or when wrapping up a separate piece like an arm, ear, or leg. It's especially handy for stuffed amigurumi, where it closes up the hole at the end that would otherwise leave the stuffing exposed.
When you finish off an amigurumi, you'll be left with a hole in the center.
To fasten off, cut the yarn, keeping a tail long enough to weave in — or to use for sewing later, if you'll need it. Pull that final loop all the way through until nothing's left but a long yarn tail. Now thread a tapestry needle onto this yarn.

Pass the needle through the front loop only of the next stitch, then pull gently to draw it in.
Keep repeating this, working through the front loop of each stitch around the last row. Doing so cinches the center closed nice and tight.
If the piece is going to be sewn onto another part down the line, leave yourself a longer tail.
If not, leave just enough yarn to anchor it by running through the body of your piece. In that case, take the same tapestry needle, insert it right through the middle, pass it through the body, and bring it out somewhere on the opposite side. From there you can trim it close to the surface.
That step wraps up the piece and keeps everything secure.