Be Realistic. Lenders have tightened up loan requirements, so you'll need a good credit score and at least some equity in your home to refinance. To figure out how much equity you have, subtract the total amount that you owe on all of your existing mortgages from how much you think your home is worth. If your credit is severely impaired or you owe more than the value of your home, you probably won't be able to refinance right now.
If your new mortgage rate seems too good to be true then it probably is. Check for hidden fees in your mortgage that will make up that suspicious difference.
When refinancing, don't take the first offer that comes around. Instead you should actively compare both interest rates and lenders.
When lenders offer a "no-cost" loan, they may include a prepayment penalty to discourage you from refinancing within the first few years of the loan. Ask the lender offering a no-cost loan to explain all the fees and penalties before you agree to these terms.