How does one get started in the REO business? And what's it like handling these types of transactions?

I would ask my broker, but she has no clue either!

Read all you can on this forum, and all your questions are likely to be answered. REO requires a LOT more paperwork, deeper pockets to cover expenses that arise, the patience to wait- sometimes 2-3 months for reimbursements, and the ability to jump through all the different hoops that each bank has without getting flustered (or without letting THEM know you are, cuz then they think you can't handle it and will pull the listing and give it to another agent). I do not recommend REO for new agents, broke agents, or those without a good supportive broker. Nor would I recommend it to anyone who has not learned a lot about basic appraisal principals, as a huge part of this job is being able to value properties very accurately.
Again, read all you can and get a well-rounded view of what we REO agents deal with regularly before you decide to jump in.
Oh yeah- have good E&O insurance- REO increases your chances of getting sued (so I hear)...