How quickly can credit be repaired?

I am just a couple years out of college, and ran into financial troubles a year ago that really messed up my credit. Now, a year later, my score is back up to 620–which obviously still needs a lot of improvement. What are the fastest ways to get my score up, and how long might it possibly take to reach 700 or higher? I have one major credit card that is paid off but still open, along with 4 store credit cards with about a $ 300 balance on each (not near credit limits). I have a car, but my mom cosigned with me on that. Any advice would be appreciated!

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