When pushing on the backhand, most players are at one of three levels:
There are several examples of "more." You can aim your racket one way, and at the last instant go another, a must learn for any advanced player. You can fake heavy spin, and give no-spin by snapping the wrist vigorously just after contact. You should learn both of these. Another option is a sidespin push.
There are different types of sidespin pushes, but what we'll cover here is the most common one: the backhand sidespin push, where the racket is going right to left at contact (for a righty).
To do this shot, start with your racket a little above the ball and to the right. You want to take the ball off the bounce, so your opponent is rushed; the more time he has, the more likely he'll adjust to your sidespin. As the ball hits the table, stroke down and sideways (right to left). Some contact the ball toward the bottom of the racket, so they can take it quicker off the bounce, or you can contact in the middle of the racket for more control. The key is to put both backspin and sidespin on the ball.
Placement is important. You usually want to do this shot to the opponent's wide backhand so it breaks into his backhand (assuming both players are righties or both are lefties). It's a tricky ball to backhand loop, and if he tries running around to use his forehand, the sidespin pulls the ball farther to the side then he's expecting.
When a righty plays a lefty, both players have the option of using this shot so that it breaks into the wide forehand. Not only is it pulling away from the opponent, but this type of breaking away sidespin often causes more trouble to player's forehands than ones that break into the body (i.e. righty versus righty). It also puts him out of position. When a lefty serves to you (if you are a righty, or a righty serving to you if you are a lefty), and serves short to the backhand, this is an excellent return, into his wide forehand.
The down side of this shot is that, because there is less backspin, an opponent who reads it properly can loop right through the ball, often off the bounce. So you don't want to over use this shot. However, done at proper times, it's a highly effective shot. It also puts one more thing in your opponent's mind to think about.
One time this shot is especially useful is against an opponent's forehand sidespin serve (assuming two righties). You can use the opponent's sidespin against him, returning and adding to his own spin as you really sidespin your return into his wide backhand.