Returning serves is everyone's biggest weakness - or at least it seems that way. To learn to read spin, try focusing just on the contact period - ignore the rest of the motion before and after contact. Imagine taking a mini-video of the split second of contact. If you do this regularly, pretty soon you'll be able to isolate in your mind the actual direction of the racket at contact. From that, you can read the type of spin. (You also have to read the amount of spin, which comes from racket speed and acceleration, grazing contact, and grippiness of the surface.)
However, you can also read spin by the way the ball comes off the paddle, travels through the air, and from both bounces on the table. You can't do this the first time you try it - it takes practice. Ideally, have a coach or player with good serves let you practice against their serves, where you focus on all of these aspects until you begin to be able to read the spin multiple ways. Imagine how the spin will affect the ball, and figure out what to watch for.
- A backspin ball goes down slightly at contact during the serve (relative to the racket), slows down when it hits the table, and floats as it moves through the air.
- A topspin ball goes up slightly at contact during the serve (relative to the racket), takes a low, fast hop when it hits the table, and drops as it moves through the air.
- A sidespin ball goes sideways in each of these steps.
- A no-spin ball does none of these things.
The receiver also needs to read the amount of spin. Against a somewhat grippy inverted rubber, this is roughly done by a simple formula: racket speed - ball speed = ball spin. What this means is that a server's racket speed at contact will convert to ball speed and ball spin; if the racket moves fast, but the ball comes out slowly, then most of the energy has been converted to spin. (It's actually a bit more complicated than this. You get more spin if you accelerate into the ball rather than moving the racket at a constant speed, but it's close enough. Plus you have to take into consideration the grippiness of the rubber, as a non-grippy surface will have less spin.)