You can also take the city bus. The #19 United Center Express runs on Madison St in the Loop from about an hour and a half before the show and there will be a bunch of buses waiting outside the arena after the show. These return buses are very crowded but the ride is not that long..
Outside these times, the regular #20 Madison bus runs 24 hours. More info about public transportation is at http://www.transitchicago.com.