Since I started consulting in a yarn shop a few days a week, I often have to suggest patterns for very new knitters - as in, first project ever. I know a lot of people favour scarves for teaching beginners, but scarves just go on and on, and even as an experienced knitter I have sometimes lost heart at the third foot of a six foot project.
Personally, I like a hat as a first project. It's quick, even a very simple design looks stylish and you can splurge on a nicer yarn since often one ball or skein is enough. But then hats are usually knit in the round and that means introducing your new knitter - already skittish - to the concept of circulars or DPNs. The upside of a knit flat hat is just that - it's knit flat back and forth on straight needles. The downside is it has to be sewn up after, and many knitters find seaming as intimidating (or more so) than circular knitting.
Personally, I think seaming is a bit of magic, especially in small hat-sized doses, so I offer this ribbed hat pattern in three sizes (child, small adult, large adult) with a cable variation. The pattern is three pages, with written instructions aimed at novice knitters, and links to tutorials for seaming and making your own pom poms.