Never, ever, ever, EVER get a credit card. You will regret it the rest of your life.
I established credit by saving cash for a couple small purchases, like tires, opening a store credit account, then paying it off the next week. I chose stores that would extend the credit with my dad as cosigner. Next I took a small loan at the bank I had used since turning 14, and again paying it off early. After that, piece of cake.
Granted, times have changed a bit. But I would never recommend a credit card to anyone.
Ask your folks for the book Financial Peace by Dave Ramsey. Best $25 they'll ever spend on you. Then read it. Then do it. It works, trust me.