Prepaid creidt cards are safer than regular credit cards. They work much like a debit card so that when the money is exhausted on the card, the card will be rejected.
Yes you can get a credit card, and it will help you rebuild your credit if paid on time. Go Google and type in credit cards for people with bad credit, you will get loads of hits.
First of all, you call the credit card company you are with and tell them you want to have your credit card cancelled, it doen't get any easier than that!!