I've been playing 1v1 using Random race, and finished my 10 placement games yesterday. This means that the automated matchmaking algorithms have now placed me in the rankings for 1v1 play. I started in the Gold League, Division 4, 37th place. As far as I can tell, leagues are platinum, gold, silver, bronze, and copper, in order. Each division has 100 players, and there are at least 8 divisions per league. Divisions don't appear to mean anything in terms of rank, so I think they're parallel subdivisions within the leagues. I haven't been able to get a good game recorded (one in which I'm not trounced), but I have some good replays, which I might record at some point. While I'm feeling pretty good as Terran and Protoss, I haven't won any matches yet as Zerg.
Yesterday, I played a couple of 2v2 games with someone I met by getting zealot-owned in 1v1. In the first 2v2, his game crashed with an error about 10 minutes in, at which point I took his zealots and my marines and wiped the map with our 2 opponents. Shared unit control works the same as Warcraft III, and I was able to control all of his units and buildings once he dropped.
In order to start up a game with friends, all you need to do is invite them to a party and jump in a game. You can also create a custom game and get all set up before allowing anybody else in if you want.
As of today, I'm ranked 42 in the Gold league for 1v1 and 18 in the Platinum league for 2v2. In 2v2, I've been playing Terran with my Protoss teammate. I get a barracks with a reactor add-on for quick marines, while he gets zealots followed by stalkers. We generally rush or defend against the opponents' rush then counterattack. If that doesn't end them, I build up to marauders and go to factory or starport to support my infantry.