That's a pretty important factor for most landlords. Unless you find an individual who doesn't ask for a credit score, or doesn't contact your old landlords, I'd say you're in a pickle until you improve your credit.
And while it only take a very short time to damage your credit, it can take a year or more to improve it significantly.
Here's the nutshell: Make every one of your payments on time for 12 months
and your credit will improve remarkably.
If you have judgements, that's another issue that has to be dealt with.
If you are in a hurry to buy/rent and there are very good reasons why you were a late pay before but
you haven't been late since your circumstances changed and you can prove it, you might have a chance at renting.
Buying ... your credit's got to be in the mid 600's for your name to be on a mortgage loan.
If you want names, numbers, facts and/or figures call me. I'll give it to you straight.