I wish I had the time to answer this properly but I will summarize a few key points.
Overall, this subject is HUGE. This, imo is one of the more complex yet least understood by developing players. It involves key points such as court position, opponent play style, opponent mechanics, aiming elements of the swing such as hips and shoulders, and lead arm/shoulder, and also ball mechanics, and even your shot mechanics.
Court position I think is obvious. Lots could be said though but I wont go into it.
Play style is important to understand. You will notice some players love to hit certain shots on certain situations. This has to be taken into effect. Someone loves the inside out forehand... then you have to watch for it. It will lead into another area of what you hit as well.
Opponent mechanics is also important. Shots they favor and their movement, general swing style like westerners don't like low balls, etc, continental's contact point is farther back in their body possibly leading to disguised inside out shots, etc.
Big factor is of course body aiming mechanics. Many players will aim with their lead shoulder. This has to be taken in consideration with their swing style and body mechanics. Someone who hits mostly open stance will have different shoulder aiming then a even - closed stance hitter.
Some more interesting things, ball mechanics... as in like what the ball is doing. This coincides with your shot making and even court properties. Is the shot going to kick up with high spin on clay? This may limit their shot making abilities and angles. Low and fast on a westerner? They will probably have to get really low and have a hard time going cross court if late.
All of these things add up to a sum of its parts. You may expect this person who is clearly aiming DTL with his closed stance to take the ball early or over rotate their hips, or even their wrist and flick it cross court on you. Maybe your opponent is very inconsistent and hits late a lot hitting inside out. Maybe they have slow footwork and hitting at them jams them making it inside out.
There are big key elements that can be dead givaways.
Footwork - a closed leading foot makes it generally difficult to hit a cross court shot. If you see a person open his foot a lot on the last step, this will give them a lot more freedom to turn.
Hips - Next come the hips which again control how much rotation a person will be capable of. Someone with very closed hips on setup is going to have a hard time going severe cross court.
Shoulders - Lead shoulder aims a shot.
Again even these big givaways are very much subject to understand what the normal baseline style is from your opponent. Someone who is very open stance western will set up very different from a closed stance and easterner.
Overall though the biggest aspect is paying attention to your opponent with your peripheral vision. As you watch the ball, you should be taking in the movement of your opponent as they strike it. Even watching their follow through with your peripheral vision as you track the ball. Seeing a follow through will help you understand what type of ball you are about to encounter. Slice, spin, how much spin, etc. The better you pay attention to your opponent, the better you will be able to predict their shots.
When you put all these things together, you realize how incredibly complicated it can be to process all this information in a split second. Then you truly marvel at the player like Frabrice Santoro who has such an incredible comprehension of this and able to process it under the fastest of conditions.