I agree with Rusty, Marta. There is no substitute for a good instructor here. There are so many variables--equipment, anatomy, technique, conditions, attitude, personal preferences--that any "tips" we give you here are shots in the dark, and may not apply to you at all. I'll fire a few generic shots anyway....
IF your technique was sound before you got the new skis, and IF your equipment is set up well for you, then you should have no trouble at all adapting to the new stuff. Indeed, it will validate everything you've already learned, make it easier, and be more fun.
You can get away with generally less effort, allowing the skis to do more for you. Make sure you begin in a balanced, centered, "neutral" stance--not leaning forward on your boot tongues, or back on your heels. If you don't already, focus on movements that steer your ski tips INTO the turn, rather than pushing/twisting your tails OUT of the turn. You can skid and brake as well on the new skis as the old (contrary to some opinions), but what they really do better is carve and shape nice round, gliding turns. You do not need to displace them much, or at all (usually), to start a turn--focus on subtle tipping of your feet and lower legs and gentle guiding of the tips into and through the turn. Focus on the INSIDE ski, to initiate your turns, and all the way through. Make sure your movements originate low--in your feet and ankles, rather than your upper body. To keep it simple, try this simple "mantra"--right tip right to go right, left tip left to go left
--and see what happens! Or practice "railroad track turns" on a very gentle (at first) slope, thinking "tip the right ski right to go right, tip the left ski left to go left." If you're good at experimenting and your technique was fairly sound to start with, these ideas may well get you on the right track.
HOWEVER--no one's technique is perfect, ever. And the vast majority of skiers, whether they know it or not, have acquired a lot of bad habits that will not let them exploit the advantages of the new equipment. Odds are (nothing personal here, and I could be wrong about you!) that you would benefit from some new ideas and some new movement patterns. As simple as they may sound, the movements and concepts I described in the previous paragraph are the opposite of what most skiers do as a habit! But even if these ARE your habits, if nothing else, a good intstructor will help you "connect" with your new skis much more quickly than you would on your own.
Also, as you noted, the new skis are far more responsive than "traditional" equipment. This means that their set up and tune are more critical as well. Again, a good instructor will be able to spot problems quickly.
So ask around to find a good instructor and request him or her for a lesson--private, if possible. (If you can't find a reliable recommendation, ask for the highest level of certification the ski school has available.) Be prepared to encounter some odd-feeling new movement patterns, depending on your current technique. Go with an open mind, ready to play!
The new skis are really not DIFFERENT than the old ones--nor are the techniques involved in carving--or skidding--turns on them. But they certainly represent an advance in responsiveness and performance, as you've noticed. They have built-in grins!
To summarize, graphically, the differences between new and old, I offer the following highly technical explanation:
Enjoy! Welcome to EpicSki, by-the-way, Marta!