I've got M&B Warband but never played multi player so far.
Where do I start?
Do I need to find a server to play on, or is there some kind of server browser built into the game?
It has built in server browser and if you buy the Steam version, you can use Steam browser too I think. Games running vanilla M&B are using module called "Native". Custom maps are downloaded automatically if you don't have them.
For starters I recommend team deathmatch or dueling servers to build up some skills. These servers have low respawn times and you can quickly join the action.