I know everyone thinks making a baby blanket is one of the most basic starting crochet items, but I don't agree.  My neighbor wanted me to teach her, I suggested starting off with dishcloths or a scarf.  They are both very useful, and make great gifts, as a baby blanket, but they are much quicker to finish, which gives the new crocheter a sense of accomplishment.  After you have done a few of the smaller items, a basic baby blanket is easy, but does take time.  Also, remember to weave in your ends, not tie knots.  This leaves your finished item much nicer looking, and also holds it together a lot better, knots tend to untie, leaving your hard work to unravel.  To weave your end in successfully, use a blunt-end needle, and weave yarn through the stitches an inch or two the opposite way you are crocheting.  Then weave in the other way an inch.