Lars, that's a great question. The common denominator in intermediate (and below) skiing is a lack of base level skills. These skiers need to begin by focusing on edging and balance skills.
Start exploring the concept of moving fore and aft on their skis. Become aware of the location of the pressure existing on the base of their foot, and learn how to control it. Play with lateral balance, get comfortable skiing in different states of balance, and learn how to alter them as desired.
In regards to edging skills, most intermediate skiers employ very energy and movement inefficient methods of turning their skis. They are uncomfortable with the sensation of tipping their bodies downhill at the beginnning of the turn, and are intimidated by the acceleration produced by turning gradually into the falline, so they rush the top of their turns with gross upper body rotary movements and pivoting/stemming actions. They need to learn the art of leg steering, and the concept of turn shape. They need to discover that the falline is their friend, not their doom,,, and come to view the speed it produces as something to be enjoyed during a temporary phase of the turn, which can be harnessed to what ever degree is desired via turn shape. They need to learn how they can employ skid angle skills while leg steering their turns to produce any resultant speed they're comfortable with, while on any slope, and while skiing any line or turn shape.
These skills alone will elevate their skiing to levels well above the majority of skiers on the slopes,,, without even beginning to explore carving. How do they learn these things? Well, that's the big question, isn't it? A training program of some sort needs to be pursued. These are not things most skiers can self discover and learn on their own in short order. Either on snow lessons with a quality professional need to be taken,,, or a structured and comprehensive self-training program needs to be followed,,, or both. Those self-training programs can be found in the form of books or video. Tips from the Internet can provide some clues of what to do, but they don't provide the detail, visuals, or feedback needed to really get a person from point A to B. Advice from friends can also provide some help, but because the technical and training knowledge of the friend is often limited it can also send the intermediate skier on wild goose chases and down dead end roads. The best and most productive route is to seek the professional advice/assistance I suggested above.
Here's a little video I put together that provides a quick overview of the common stages of maturation in edge control skills.http://www.youtube.com/watch?v=2Fs2jkOA74o