Find a easy to deal with Realtor that you trust. Ours works in a 'team' enviroment and in our case it seemed to work out well. I enjoyed the differing points of view and the ability of another team member to offer up an opinion when our Realtor 'wasn't sure'.
Treat an REO just like any other property. Don't assume the price is good just because 'it's an REO'. Do your own research on comparable property prices and balance that with your Realtors assesments. When negotiating, don't be afraid to ask for some things that you might ask of an actual 'owner/seller'. Banks have the exact same goals as real people. The best price and a fast sale. They will make the same concessions as 'real owners' to make a deal. It seems, from many posts in many places, that as far as REOs are concerned a 'clean contract' is sometimes worth more to a bank than the price. Espcially contingencies. Banks want to make sure they are not wasting thier time and once they enter into a contract that want it to close. If your a renter, don't have a home to sell first and have good credit for easy hassle free financing your probably golden.
As far as research goes...I feel it helped me considerably. I pretty much spent every night for 4 months browsing the internet for info. Listings, mortgages, escrow, FHA, recently solds, etc, etc. I even googled up the listing realtors to see if I could glean any information. I feel it paid off. We got somethings even our Realtor was suprised at. Money for repairs on an 'as-is', for example. I can't say if was my newfound info or simply todays market conditions that helped us get into our home. But, everything certainly helped.
Find an experienced realtor - experience counts.
Learn the market so that you know what a good deal looks like. Many REOs and short sales are still over-priced. However, properties that are priced right go quickly - within a month. Have your agent check the comps and be ready to act quickly when you see a good deal. On my blog at http://sandiegosfinestrealestate.blogspot.com I just wrote an article on my analysis of foreclosures and short sales in San Diego. Kep points of interest are sales prices with respect to list prices and old list prices.
In order to act quickly, you must have all your loan paperwork in place. First you should already be pre-approved with your lender of choice. Also many REOs and short sales are requiring loan pre-approval with their own people - so be ready to have your entire loan packet emailed when you do find the property you like.
As Robert said you must be ready with a pre-approval letter when you are ready to place an offer on an REO property. You must be diligent in your research, know the location where you want to live, know what you want in your home and know your budget. A lot of REO homes need plenty of work, so you must dig deep into these properties. These homes may have low list prices, but there is a good reason.
Transactions on REO properties can normally be completed much quicker than short sales listings.
Jess has given you good first hand experience and some excellent advice.
My advice is be diligent and work with an agent that can guide you through the transaction smoothly.
Happy House Hunting!