Minimum payments are often set very low, so it could be years before you are debt-free if that is all you pay.
New credit card legislation now requires creditors to indicate on your monthly statement how long it will take to pay the debt. Look for that information and plan to pay your debt sooner. How? Paying more than the minimum! You may be able to delete your debt by the end of the year or, at the very least, make a significant dent.
If you have multiple accounts, focus your extra payments on one creditor at a time. Many people like to start with the debt with the lowest balance because it can be paid off the soonest.
However, you will save the most money by starting with the debt with the highest interest rate. If you cannot pay extra on a regular basis, try to do it when you receive periodic income, such as a tax refund or bonus.