In my experience, usually you want to emphasize your strengths, even though you have bad credit. Offer the landlord or manager to see your bank statements and income information. This usually exceeds their needs for good credit tenants.
I am a property manager as well as an agent and I review rental applications daily. Here are a few tips to help get your application approved even if you don't have great credit. I suggest writing a cover letter with an introduction about who you are, why you love the rental you are applying for, and an explanation why you are moving. You should get a letter of recommendation from your current landlord to show your rental record of paying on time.
Many times people with bad credit will have a local friend, or family member act as their guarantor. It makes me feel more comfortable because I make sure the guarantor has ample income and good credit. You can always offer to pay a double security deposit or pay a few additional months of rent in advance as well.
Each landlord will set their own criteria as to what they will accept. Many people have had difficulties over the past few years resulting in foreclosures and bankruptcies, but have still found rentals available. You may need to be more flexible in what you will accept, pay or be required for a deposit, but there should be options for you.