I've been playing 2, 3 and 4 player matches online. You need to be within range of a wifi point that you DS has been set up to access. Players all take their turns at the same time, which keeps things moving but can lead to lags when people are involved in combat or diplomacy. (In fact, player to player diplomacy seems very odd - you'll often be told that the other party is unavailable - perhaps this is when they are watching a fight - occasionally even when you've not attempted to talk to them.) At the start of the game, you can set if turns will be fast, normal, or slow, which basically means that when one player declares their turn over everyone else gets a countdown to finish theirs - again, keeps things running, and also acts as a nice handicap for anyone lucky enough to build a massive empire.
There is also a DS LAN option, which again uses wifi but only to directly connect a group of players with their DS consoles and no internet connection required. I've not tried it yet, but I do know that I've played on a DS LAN with a couple walls between me and my friend before. You get a little icon telling you your signal strength, so you can tell if you're too far away.
