Fundamentally once you see the ball curving you just have to anticipate it and make adjustments.
One of the most common places to see it is from a low slice. Just like on a sliced serve, you have to position yourself to allow for the slice. From a low, bh slice for example (a rightie to a rightie), if you're going to take the shot as a fh you have to let the ball come at your body so by the time it gets to your racquet it's moved off to the side into your hitting zone.
The side spin balls that are harder to hit are the ones that kick on the bounce differently than they were slicing in the air - kind of an American twist groundie. You see these on occasion, especially off of higher balls. You just have to keep your eye on the ball and watch it. If the ball kicks in some unanticipated way it you just have to deal with it.
And this is one of the bigger reasons why all the spin in today's game is more than just about keeping the ball in. All that spin makes the ball kick in ways that mess with your opponent. Combined with the fact that the ball is going really fast, it can get really hard to get a clean hit sometimes. Then you have a weak ball that can be attack.