Lenders like pristine credit reports. If you have a bunch of open credit card accounts that you never use (and who doesn't?), consider closing them. It will boost your credit score and make you a much more attractive borrower to a lender. Then, a month after you've closed your accounts, go over your credit report with a fine-tooth comb. It should read that the accounts were closed at your request. (You don't want lenders to think someone cut you off and that you're a bad credit risk.)
When evaluating different lender offers, in the mortgage loan pre-approval process, pay closest attention to the interest rates they are offering & the closing costs. These are the two biggest factors that will help you figure out which lender is right for you. If one of these two factors is too high, it could offset the benefit of refinancing for you.
You can also save money on your mortgage refinancing by paying "points." This is a fee that effectively lowers the interest rate of your loan. If you plan on staying in your home for a long time, this long-term strategy can be an excellent way to save thousands of dollars.
Weigh the costs carefully of how long you will be staying in your home vs. how much of a savings you will be getting in a refinance. Make sure you include closing costs in your decision.