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The advice I followed from here was know and fix what is negative on your credit report (plenty of threads regarding that on here) 2nd use the cards you currently have wisely, meaning pay the balance in full every month and keep utilization under 30% then just WAIT (this is hardest thing, took me nearly 10 months). This really worked for me When I started I could not even get a lousy retail card approved with the 8 baddies on CR and scores in low 530's.
One of the most valuable techniques I've picked up from these forums is that as much of a snowball effect bad credit problems can have, good credit behavior can have an equal snowball effect. To keep it simple,
Build a reasonable stable of cards.
Keep your utilization low and your scores high (NO LATES, let your old lates age out!)
Take advantage of soft pulls to grow those credit limits -- the higher your limit, the easier it is to maintain a low utilization % while still occasionally carrying a balance.
Eventually you'll get into the territory of premium cards. I'm not there yet, but I'm playing the game right, and reaping the rewards, so I know it's just a matter of time.
The catch is, by the time you get there, you no longer need low interest cards, because you've already moved into the habit of not carrying balances.
I have some "premium" cards with average to low average scores
Honestly I do not even know the interest rate they are because I KNOW I will never not pay in full
Every approval I have was on 1% utilization