One of the best ways to quickly build a payment history is to use a credit card. A secured credit card can help with this step if your poor credit precludes you from qualifying for a “regular” credit card. A secured card requires that you keep money in a linked savings account as collateral. Because the money is already there, it is easier to get approval for a secured card — especially when you have poor credit. In either case, your payments are reported to the bureaus every month, so it makes a big difference in showing that you pay regularly — and on time. (See: Wise Bread's review of the 5 best secured credit cards.)
This is easier said than done, but reducing the amount that you owe is going to be a far more satisfying achievement than improving your credit score. The first thing you need to do is stop using your credit cards. Use your credit report to make a list of all of your accounts and then go online or check recent statements to determine how much you owe on each account and what interest rate they are charging you. Come up with a payment plan that puts most of your available budget for debt payments towards the highest interest cards first, while maintaining minimum payments on your other accounts.