In the standard random drill, one player (the "feeder") plays backhand (or forehand) randomly anywhere while the other player (the "driller") keeps it to his backhand (or forehand). There are really two things going on here, as both players are actually doing a drill.
For the "driller," he's reacting to ("neuromuscular adaptation"), moving to (footwork), and stroking (technique) the ball. He's also learning to recover from the placements of the feeder. This is one of the most game-like rally drills you can do. Do the drill regularly and it becomes instinctive.
For the "feeder," it's key to remember that he's also doing the drill. However, his focus is on consistency and placement. Consistency is key, as with all drills. However, to get the most out of this drill, focus equally on placement. This is where you learn to go to the "three spots" - wide forehand, wide backhand, or elbow (midway between forehand and backhand). But it’s not just randomly playing the three spots – this drill allows players to learn what combinations work. For example, when you go at the middle, it forces the opponent to move out of position to play forehand or backhand – and so one of the corners open up. Sometimes the player overreacts to cover the open corner, and so the other corner is the one that opens up. This drill allows the backhand player to learn how best to maneuver the opponent around. Do the drill regularly, and it becomes instinctive.
In both cases above, the key phrase was "Do the drill regularly, and it becomes instinctive." When it becomes instinctive, you'll do it in a game, and your level will shoot up.