Now that you're an expert on steering out of a skid, we're going to take away two of your wheels. This, according to Ray Pierce of the Team Oregon Motorcycle Safety Program, is a whole different ballgame.
First of all, a rear-wheel skid in a single-track vehicle (which is what motorcycles and scooters are) usually happens because the rider is using too much rear brake around a turn, not because of a slippery surface. Second, a single-track vehicle in a skid has no steering control and no direction. Your job as rider is to get the wheels back into alignment.
Imagine you're looking at a bike travelling along the street from high above. You're in, say, a hot air balloon. A turn is coming up, and the rider pulls too hard on the rear brake lever. The front wheel rolls straight ahead, but the rear wheel -- the one with the brake acting on it -- follows the line it was on. The bike is leaned a bit for balance, so the rear wheel "steps out on the high side," to use Pierce's words, which sound a bit like an old-timey dance move. What he means is that the rear wheel is out of alignment with the front wheel on the outside of the turn.
Just like with a car, you steer into the skid in an attempt to bring the wheels back in agreement. Release the rear brake to let the back tire roll and don't reapply it until you've got traction. Even then, you'll want to squeeze that brake lever gently. If the bike straightens up too quickly, the rider can be spit out of the saddle. That, says Pierce, is the worst-case scenario.
Pierce says he spends a lot of time teaching riders how not to get into a skid in the first place -- the best-case scenario. He remembered getting into a skid himself on a go-kart track not long ago (proof that even the pros make mistakes) and he didn't move anything on the bike. He just hoped the rear end stayed underneath him while he brought it back to upright. "There was a lot of praying," he says.