If you don't mind running minisat as an external process you can get started very quickly. You just need to dump your problem to a file in DIMACS format (see Google). Running it once or twice manually should give you a clear idea of how to interpret its output.
If you want to use it through the API, you'll have to do more reading. As far as I know there is no tutorial or quick-start guide, but the main paper linked from the
MiniSat page [1] is a good introduction to the interface. You'll still need to look at Solver.h to see the latest version of the interface. You'll need to link to libminisat.a, which you can build by just running "make libminisat.a" in the core subdirectory on Unix-type platforms.
[1]
http://minisat.se/MiniSat.html-- Nathan