Sport fitness advisor is a good site for abs/core exercises. Here are some examples from their site:
Check out their site for more exercises!
My personal recommendation: get a swiss/exercise ball, start off with no weights and focus on the tension in the core. I'm assuming when you say bigger muscles, you mean a six pack - Six packs are hard to come by and are seen on people who have very little body fat, the abs are interlaced muscles that are one small part of the core.
Your question about hurting yourself - Yes, just like any other exercise, you can hurt yourself if not done properly. Technique first, then add intensity. A good, consistent, complete body routine is what the focus should be on.