Have you ever studied your opponent to see exactly when in his strokes he commits to a specific placement? There really are two important points in the swing.
The first is when the opponent has committed to the placement, but you don't know where yet. Normally you would not react to this, but sometimes, against a predictable opponent (which means most players), you can anticipate. For example, if you serve a deep breaking serve to an opponent's backhand, most likely he'll return it to your backhand. So you might anticipate this, and at the instant when the opponent has committed his direction - but hasn't actually telegraphed the direction - you might anticipate his return by stepping over to attack with your forehand. Don't overdo this, but it's a definite tactical advantage if you can do this sometimes.
The second important point in the swing is when the opponent has telegraphed where his placement will be. You should learn to observe this so you can move the instant you can see the direction. Many players don't move until the opponent has hit the ball, but for the large majority of players, you can see where they are going by the time they start their forward swing. At the higher levels, many players learn to hide their direction longer and to even fake one way and go another, so against players like that learn when they have really committed.
The shoulders are often the giveaway for where a player is going on the forehand. Many players line their shoulders up early to hit crosscourt or down the line, and it's like they have a big sign across their shoulders saying where the shot is going. When you first learn the forehand, this is fine, but as you advance, learn a little subtlety and deception. For example, from the forehand side, rotate the shoulders way back as if you are going down the line, then at the last second whip about and go crosscourt. Or set up to go crosscourt, and at the last second rotate the shoulders back more so you can go down the line. Or simply cock your wrist back at the last second and go inside-out down the line. These are easier shown then explained - have a top player or coach show you how to do these shots.