Pull your credit report from the bureaus and review it for any negative items (late pays, collections etc) and inaccurate detail. Try to dispute negative items and remove them from the report. If required pay off any unpaid debt. Otherwise, you won't get a low rate and may not even qualify. Of course there are lenders in the subprime market who may offer you a bad credit refinance loan, but it's better to avoid them as they'll possible charge higher rates and fees.
Closing costs can be expensive. If you plan on refinancing your home to save money, be sure to take into consideration how much the closing costs on the new loan will cost you.
If your monthly payment on a fixed-rate loan includes escrow amounts for taxes and insurance, your payment each month could change over time due to changes in property taxes, insurance, or community association fees.
If you plan on moving out of your existing home within the next few years, it may not be beneficial for you to refinance. Make sure you let your mortgage specialist know your future plans.