It is worth actually understanding spin in the first place.
On a pure topspin ball, the ball will arc down towards the table. If you try to contact the back of the ball or the bottom of the ball (like for chopping or pushing), the ball will POP UP. You know what to do with a topspin ball right? Usually, covering the top of the ball causes the ball to propel out instead of up and the incoming topspin will add to your power if you do that. If you have your racket at the right angle as you cover the top of the ball and you don't even move your racket, the ball will go back and be a decent shot: that is called a block. That is what blocking a topspin shot is, right: using the momentum of the ball and the spin on the ball to propel the ball back because you touched the ball in a way that compensates for the spin on the ball.
On a pure backspin ball, without gravity the ball would arc up. However, because of gravity, a backspin ball has a kind of flat tradjectory (gravity is trying to pull the ball down and the spin is trying to cause the ball to arc up - that combined causes a flat trajectory until the ball loses pace and starts to fall). On a backspin ball, you already know that if you contact the back or the top, the ball will get Pulled DOWN. If you contact some part of the bottom of the ball, that will propel the backspin ball forward and the backspin on the incoming ball will give your ball some pace and add to your backspin. This is also why, on a push vs heavy backspin, if you touch the ball lightly in the right place, the ball will just do the rest and go over the net with a pretty good amount of backspin without you adding almost any forward momentum force to help the ball go in the direction you are guiding it.
So, to sum up: if the ball is curving down as a result of the spin, you cover the top of the ball if you want to compensate for the spin; if the ball is trying to curve up against gravity, you contact some part of the bottom of the ball if you want to compensate for the spin. Right? And then if you understand this, there are hundreds of things you can do to the ball to change the spin that you send back including going against the spin and having your stroke angle compensate for the spin while going against the spin instead of going with the spin: A loop vs backspin is an example of this. Someone who knows how to push a topspin serve with heavy backspin is also an example of this.
But for the simple concept to get started feeling what to do, think about this based on the above information:
1) If the sidespin on the ball causes the ball curving towards your FH side, how would you contact the ball to simply put your racket out and compensate for that sidespin?
2) If the sidespin on the ball causes the ball to curve towards your BH side, how would you contact the ball to simply put your racket out and compensate for that sidespin?
Think about it.
If you really think about it, then it will open up many ways you can respond to those serves that are giving you trouble.