So here is tip I learned from a wise person once--
When you have extra money to use towards paying credit card debt, use that extra money on just one card. Pick the credit card you have the lowest balance on, and then work towards paying it off completely. Send in extra money along with the minimum monthly payment, as often as you can, until that card is paid off.
Then start paying off the next credit card the same way. Use the money you would have sent on the first card, the minimum payment due each month, along with the regular payment you send in each month on the second card, and you will get that card paid off faster too.
Move on to the third card. Keep budgeting credit card payments for the first two cards that you have already paid off. Just use those monthly payments for your third credit card now. You should see the credit card get paid off much quicker now.
The key is: when you pay off a credit card, and no longer have a monthly payment to make on your card, don't just spend that money elsewhere. Keep that budgeted payment and use it to pay other debt each month.
Keep doing this, one card at a time, until all are paid off.