How do I pay down credit card debt.?

I have credit card debt of about $6000-$7000 on 5 credit cards. I'm getting married next Feb. and really don't want to bring my debt into my marriage. I have student loans that are feasible to pay and I don't mind bringing that into my marriage. I have a car that getting old but still is reliable and would like to replace in the next year but am currently not in a rush to. My question is do I pay the mthly balance and work on paying one credit card off per mth. Most cards have a balance of $1000 or less. I make about $1250 a paycheck and will be picking up overtime this summer. What is a good way to pay down this debt?