The Falkenberg Drill (also called the Two-One Drill and the Backhand-Forehand-Forehand Drill) is probably the most popular drill for players at the intermediate and advanced levels. It combines three of the most common moves in table tennis: covering the wide forehand, covering the wide backhand, and the step-around forehand from the backhand side (since you often want to end the point with your forehand against a weak ball to the backhand). Go to any major tournament and you'll often see the top players warming up with this drill.
The drill was popularized by 1971 World Champion Stellan Bengsston. While he was developing as a player at the Falkenberg Club in Sweden in the 1960s, one of the most common drills was forehand-backhand footwork, where a player alternated hitting a backhand and then a forehand from the backhand corner. The problem was this only practiced one of those three common moves - the step-around forehand - and half the drill was following a forehand from the backhand side with a backhand, which isn't as commonly done. Stellan made the Falkenberg Drill central to his training, and soon players around the world took notice.
In the most common way of doing the drill, you keep returning the ball to your partner's backhand. Your partner hits two balls to your backhand, one ball to your forehand, and then repeats the sequence. You return the first ball with your backhand, step around your backhand corner and return the second ball with your forehand, then move to your wide forehand and return the third ball with your forehand. You should use the same strokes in the drill as you want to do in a match - hitters should hit, loopers should loop. Many loop the forehand and hit the backhand.
There are many variations. You can start the drill off backspin with a loop, and then continue. You can either hit or loop the forehands or backhands. You can do the drill to your partner's backhand or forehand. You can have free play after a certain number of repetitions, such as after three (nine shots). Or use your own imagination and make something up. Or just use the basic standby, as described above, as many do.
The drill can also be done with multiball. This allows a player to maximize how fast he can do the drill, since miss-hits by either player no longer affect the drill.
A key factor in the drill is balance. If you are even slightly off-balance at any time, you'll have trouble recovering for the next shot. When I say "off-balance," I don't mean actually stumbling-around off balance; if your center of gravity goes outside the area between your feet, or even goes too much on one foot, it'll slow down your recovery for the next shot. The most common problem here is letting the weight go too much to your left (for a righty) when playing the forehand from the backhand side. It is this constant state of balance that allows top players to seemingly get to every ball since balance is the key to getting a quick start. So keep your weight between your feet.
Here are some examples of the Falkenberg Drill. Watch, learn, and become a Friend of the Falkenberg!