I agree with lauralaylin. A lot of knitting or general needlework stores offer classes, and that's a great way to learn. Or see if you can find a relative or friend to teach you; I learned from my mother.
I knit mostly simple projects. The most complex thing I've knitted is a cardigan. I'm currently working on a baby blanket for a friend of mine who's just had her first baby... it's a 4x3 grid of 12"x12" squares. (The squares are knitted; I just have to get around to sewing them together, hopefully before the kid goes to college.

) If there's anyone close to you who's expecting a baby, that's a great project. Or, you can make a 4x6 grid of 12"x12" squares as an afghan. You can knit every row (garter stitch), alternate knit and purl rows (stockinette stitch), or try a simple pattern like ribbing.