Rental applications are similar to mortgage applications. Landlords and property managers are looking for security as well as responsibility. They want to know you will be there for the term of the lease and hopefully several years longer. So:
Make sure you pay all of your other bills and obligations, credit cards, personal loans, insurance payments, utilities, etc., ... on time. This will lessen the negative effect foreclosure has on your credit.
If you are working, do not change jobs. If you need to change, stay in your current field.
Also, now that you are not making your house payment, begin to set aside some cash for first & last month's rent and a security deposit. An extra $500 added to the securtiy deposit might make the difference between getting and not getting the property.
Begin looking for a rental a month before you need to move. "I need a place by this weekend" is a big red flag to a property manager.
I have some info from a credit councilor and a local mortgage broker that outlines the effect that foreclosure, short sale, or bankruptcy will have on your credit. Check out my info and, if you are interested, send me an email through Trulia and I will forward that to you.
Don't worry about the process, you are going to get through this and it will all be OK!