How do you get rid of your credit card debts?

It depends. Obviously the best method is to pay them off completely. If you can't do this, then try to make as large payments as possible- much higher than the minimum payment.

If you can only make the minimum payment, or are struggling to do so, realize one fact: if you have $10,000 of credit card debt, and your average interest rate is 18%, it will take 13 years to pay-off! (see creditcards.com). And the above figure doesn't take into consideration various fees or unpaid interest.