1. Engaging your abdominal/core muscles is necessary for maintaining good alignment during the turn.
2. Every turn is a balance, so work on balancing in the position you want to turn in (retiré, a la seconde, etc.)
3. Spot and keep your eyes off the floor (or that's where you'll end up).
4. Use only enough push to get around - sometimes a dance student's biggest downfall in pirouettes is pushing so hard that they throw the turn off.
5. Connect your arms to your back - you should feel width between the shoulder blades and the arms should maintain their position (don't "wind-up" for a turn)
6. Take off from a properly placed and wide plié for power in the turn.
7. Strengthen your ankles supporting the relevé - if you are wobbly, sickled, or pronated, this will ruin your turn.
8. Make a choice to come down from the turn, don't let gravity make the choice for you.
9. Picture yourself doing a beautiful, clean pirouette - it really does help!
Pirouettes are not an easy movement. Anyone can whip themselves around but it takes years of practice (plus a good deal of strength) to perform a proper pirouette. Work hard at the barre and in centre on the fundamentals (plié, relevé, etc.) And, work on getting a good, clean single first (with all of the elements above), then progress to multiples. Good luck!
Good Luck :]