There are many types of pirouettes, turned in, turned out, en dedans, en dehors, leg out to the side, in arabesque, arms every which way, but for today we will only address the classic turned out ballet pirouette en dehors.
This pirouette will be in a passe position with the arms out in front of you, turning towards the leg in passe. About.com has a wonderful step by step description of how to do this pirouette.
What I would like to share are some exercises that you can do at home that will help your pirouettes. The first exercise is a "spotting" exercise. Spotting is important because it will both keep you from getting dizzy whilst turning and also give you the momentum needed to complete a turn. The video below demonstrates the spotting exercise.
The next exercise deals with the "passe" position. To have consistent strong pirouettes, your "passe" must also be consistent and strong. The most common problem (that even the greatest ballet dancers have) is leaning forward, backward, or even to the side in their passe position. You want to have a strong center and keep your torso as straight as possible. The correct position is demonstrated by Colleen here:
Of course having a teacher or outside eye can help you know which way you tend to lean, but you can also tell for yourself. If you fall out of a pirouette, notice which direction you fall - that is most likely the direction your are leaning. If fall backwards, you are leaning back. If you fall forward, you are leaning forward. If you fall to the right, you are leaning to the right, and if you fall to the left you are leaning towards the left. To help compensate or "fix" the problem, think about leaning the opposite direction. (I.e. if you fall back think about leaning forward. If you get to a point where you are now falling forward, you took the correction just a little too far, so bring it back a bit.) Don't get frustrated, it's a career long struggle that all those dancers at performing at Lincoln Center grapple with. You are not alone!
Here is an exercise you can do at home to strengthen your passe position!
Lastly, you don't necessarily want to start out by working on a full pirouette. If you looked at an aria or concerto you would break it down into sections. You can do the same with a pirouette. Here is how:
*While "pirouette" means to "twirl" in French, if you think about "twirling" you will most likely have a really great time, but not a successful pirouette. So, spot spot spot!:)