Resistance bands are a great way to begin your strength training routine. And they aren't just for beginners. I know body builders who use them as part of their training routine too. I've been using them for years.
Most exercises that a person can do with hand weights can be done with resistance bands. Where to start ? I would start by joining SERGEANTMAJORs resistance band team. He's got a bunch of beginner to advanced routines posted. www.sparkpeople.com/myspark/groups_individ
Some exercises that you could do with the bands include rows, lateral raises, front raises, shoulder presses, chest presses (you'll need a study post to wrap the bands around to do that), squats with the bands, bicep curls, dead lifts, etc.
NOTE, this trainer is using a circular band. You can do the same things with ones with handles. www.youtube.com/watch?v=mv0sEeAUSTY