For some reason, American coaches tend to de-emphasize the slice (and also, it's cousin, the chip). Perhaps, it's because these are not seen as forceful shots and we tend to view ourselves as an aggressive nation - always taking the game to the opponent. Maybe it's because so many of our players utilize a two-handed backhand. Nevertheless, slices are one of the most effective weapons (uhmmm.... Federer???) that a player can hope to master but the player will be successful only through lots of practice as the preparation, grip, stroke, footwork, balance, finish, etc. is quite different than on a topspin. The player should learn not only when and how to hit a slice but also when the slice is inappropriate.
For example, a properly executed slice tends to skid and stay low. This will force the opponent to bend under the ball and strike it in a completely different manner than a topspin. Whereas the ball rotates "top-wise" into the string bed, the slice actually rotates (or seems to rotate) backwards in the same direction as the "brush" of the string bed. The two forces combined often result in the ball going into the net. In addition, slices are great for taking time away from the opponent (since they tend to clear the net by only a few inches) or, if struck in a certain way, provide you with more time to recover. Furthermore, a knifing cross-court backhand is great to combine with a heavy, exploding cross-court forehand in order to yank the opponent around the court. On many occasions, the rotation of the ball can also cause the opponent to either miss a volley or pop up the ball. It's not always a bad idea to slice to a net-rusher.
The key element to the slice is to have a strong forearm. The slice (chip or even the volley) is not a "swinging" shot; it's a "leaning" shot in that the player leans (with the shoulder in front) against the opponent's ball for purposes of utilizing the opponent's pace. To execute a proper slice, try to finish with the racket towards the intended target in a crisp manner. The best way to practice this shot is, unfortunately, against the backboard. I say "unfortunately" because not many players make the effort to utilize this awesome training tool. Hitting hundreds of slices against the backboard will develop strength (in forearm), feel and control. Furthermore, you will notice that the slice is more effective on lower shots (below the waist) as opposed to high balls (over the shoulder). As a rule of thumb, unless I'm trying to purposefully alternate the spin, I will try to slice almost exclusively against low balls. Balls around the waist should, generally, be belted. Also, high balls are difficult to control with a slice (or chip) because the face of the racket is open to the sky which risks sending the ball long. Again, these are shots that should be top-spinned more often than sliced. However, with practice, you will develop deadly accuracy with the slice enabling you to open up the court for the rest of your weapons.
Once you master the slice, try having some fun with it by combining it (if the play calls for it) with a heavy, short-angle cross-court forehand. Maybe slice down the line to your opponent's forehand/strength in order to open up the weakness. If you get good enough, the slice may actually get to curve outwards (i.e. away from the middle); take an aggressive step inside the baseline and pound the next stroke into the open court.