Here's the exemplar I made to show my crochet students. I've created exemplars of a number of different patterns that use only single crochet, double crochet and chain. So after I teach someone the basics, she can pick out a pattern that appeals to her.
Here's a shawl I made with this pattern, along with a closeup of the shawl.
This is an absolute beginner's crochet pattern. It uses nothing but single crochet, double crochet and chain - and it is always easy to know what row you're on and what you need to do.
Click here for the pattern (PDF format).