Before we start, here are two videos to watch. Here's a video (1:18) of a Ma Lin of China (shirtless) demonstrating his "ghost serve," where his high-toss serves almost slam backwards into the net due to the extreme backspin. Note how open his racket is. He's not only contacting the bottom of the ball, he's contacting it slightly toward the front with an extremely open racket, with the front slightly higher than the back, and essentially scooping the ball up. (More on this below.) Here's another video (1:21) that shows more clearly how to do this ghost serve, with a lower toss (and so the contact is more under the ball rather than slightly in front). How are these two able to create so much backspin?
First, you must learn to graze the ball very finely. This takes practice, and is where most players are lacking. Too often they let the ball sink into the sponge, and so much of their racket speed turns into ball speed. Instead, you should graze the ball so finely that you struggle to get the ball over the net. A key here is that contact should be on the bottom of the ball, with your racket roughly parallel to the floor. If you contact it toward the back, as most players do, then you'll likely sink the ball too much into the sponge.
Second, you must have racket speed. This comes from the arm and wrist (though with some serves, such as a pendulum serve, you use your body as well to get the arm going), with the wrist most important. The arm should drive toward the ball, with a vigorous wrist movement right as you contact the ball. As the racket approaches the ball, you should snap the arm and wrist as if snapping a whip.
Third, you can get extra backspin with a higher toss. This is because the ball is coming down faster, and you can convert that speed into spin. To do so you must contact the ball not only on the bottom, but even a little bit toward the front of the ball, with the front of the racket slightly higher than the back. This scooping motion seems unnatural to players at first, and makes it tricky to keep the ball low unless you graze the ball very finely, with a contact point very low to the table. The higher toss comes at a price - you lose some control - so you should first perfect your serves with a lower toss (head-high or so) before going for higher tosses. Many or most world-class players prefer a lower toss with slightly less spin because of the increase in control as well as being able to do more deceptive motions in the increased time as the ball goes by.
Fourth, the grippier your racket surface, the more backspin you will get.
A truly heavy backspin serve that stays low and short is extremely difficult to attack, and so you'll get lots of passive returns (pushes) that you can attack. Players are not used to so much backspin and so often put it in the net. Combine with other spins (including no-spins), and you will create havoc with your opponents.