There are literally thousands of mortgage companies all over the country. It is important that you choose a reputable one. Most reputable companies will be part of the Better Business Bureau or other community watchdog group. Good companies will also have websites that rank well on search engines such as Yahoo and Google.
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 you are refinancing from one ARM to another, check the initial rate and the fully-indexed rate. Also ask about the rate adjustments you might face over the term of the loan.
Calculate the financial benefit of refinancing in one, two, or three years. Does the benefit compare with your plans for staying in your home?