Depending on the person credit cards can be extremely evil or a decent tool to get some sort of return. Find a card that has some sort of straight cash or equivalent money (REI or the like) as a return. If you can pay some bills with it on a regular basis and keep the balance at zero while having solid income, that will definitely crank your score up. If you can't maintain control to keep a zero balance you're in for a world of hurt.
I have the REI card and pay bills with it, then immediately pay off the card with the money I had budgeted for the bills anyway. I usually end up with a hundred dollars or so in "free" REI money every year. My favorite trick? If I have a large purchase to make at Home Depot, Lowes, or whatever I will buy gift cards at Safeway with my REI card. Then I get gas points for cheaper gas along with the money back on the card, all for the same expense I'd have to make anyway.