I can't manage balls with lateral effect. Can't receive them, can't generate them.
With a backspin ball, to compensate for the spin, you touch the bottom of the ball which propels it forward (instead of down). Without gravity a backspin ball would curve up. With gravity it ends up having a flat trajectory because the spin is trying to get it to curve up and gravity is pulling down.
With a heavy topspin ball, you contact the top of the ball to keep the ball from popping up and that helps you project the ball forward. A topspin ball curves down towards the table.
So, in both instances above, to do the simplest thing and compensate for the spin, you contact the side of the ball that the spin is causing the ball to curve away from: backspin, the ball would curve up without gravity: you contact the ball from under. Topspin, the ball curves down so you contact the top of the ball.
With a sidespin ball that curves towards the FH side, you would want to contact the side of the ball on the BH side.
With a sideespin ball that curves towards your BH side, you would want to contact the side of the ball on the FH side.
What exact spot on the side would depend on a number things including how much spin is on the ball.
Now, this is not the only way to handle spin. That is simply how to compensate for the spin that is on the ball so this would be the simplest way to start to learn to handle different variations of sidespin.
A good player should be able to push topsin and loop backspin; and go right at the heaviest part of a sidespin and add to it. But to start out, if you can't handle sidespin, it would be worth first learning how to see it and compensate for the spin (path of least resistance).
Corkscrew spin is more complicated and I am not going to bother with it because it is kind of a whole different subject and it is fairly rare.