Be Patient. Processing all of the paperwork that's required for a new loan takes time. Be patient while your loan moves through the system. Protect your credit score by paying your bills and making your mortgage payments on time and not taking on any more new debt than you absolutely have to.
Be Prepared. You'll probably be asked for more information and documentation after you submit your application, but before your loan is approved be prepared to document your income and assets. Answer any questions and fax documentation to your loan representative as soon as possible.
If there are only a few years left on your current loan, it's no use refinancing with a long term loan. You may need extra cash but with a long term loan, you'll end up paying more for the entire loan term.
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.