I've been volunteering with "wilderness" search and rescue for around four and a half years now. My first year was in a much more urban/suburban setting outside Pittsburgh PA, since then I've moved to West Virginia and now do much more rural/woodland searching but it would still be a stretch to call most of our search areas "wilderness."
Basically, there are two schools of thought for the organization of SAR... One puts you within a large response framework of other first responders including local police, fire and EMS, the other results in SAR being THE response agency.
The first mentality is much more common on the East Coast. On a typical search, I will either get pulled into command to help plan or coordinate operations, or will get sent out to lead a team of local personnel. You might end up with 10-15 trained searchers and dozens or even hundreds of untrained personnel (either other first responders or local volunteers) in which case you likely end up as the only trained searcher in a group of 4-5 sent out to complete a specific task.
The other system is basically that when someone is lost or missing, that SAR is pretty much the only resource utilized. A SAR team's officers would be coordinating and sending out their team members in groups of 2-3 to complete the tasks. This is much more common West of the Mississippi but is also a model seen on the East Coast as well.
The type of training you will need and receive will depend greatly on where your SAR team fits into local resources, but the one thing that is probably important to brush up on no matter what is your land navigation skills... If you have a GPS, make sure you know all of the ins and outs of how to use it. You should also be comfortable with "manual" navigation using map and compass: be able to tell where you are on a topographic map by looking at surrounding terrain, be able to navigate between two points, follow a compass bearing, plot coordinates on a map, etc.
Good luck! Search and rescue can be really rewarding, and is fascinating if you're interested in emergency management because it is one discipline that almost fully utilizes ICS in just about every callout, large or small.