Because a double pirouette will require more momentum than a single pirouette, the preparation, or the set up, for the dance move must be perfect to acquire the needed momentum. Begin with your feet in first position, then tendu, or stretch, one leg to the side as you move your arms to second position. As you bring your legs back to either fourth or fifth position, plié, or bend, your legs as deeply as possible without lifting your heels from the ground. A deeper plié than you take in the preparation for a single pirouette will be necessary.
Keeping your form perfect throughout the turn will prevent you from slowing down your momentum. Therefore, practice with single pirouettes until you can easily replicate the ideal pose of keeping your foot to the opposite knee while en pointe. This will require strong thigh and feet muscles, both to keep the leg up and to use the opposite leg for support; various exercises, such as squats and relevés, can help you to build these muscles.
A proper preparation and keeping perfect form will allow you to build enough momentum to add another pirouette to your single pirouette. However, the key to keeping this momentum is not to change anything, from your leg positioning to your arms, as your body begins to make the second turn, or the excess movement will slow you down and prevent you from making a full second turn. The one exception to this is your head, which will help carry the momentum around for the second turn as you "spot."
Proper spotting, or head movements, will complete your perfect double pirouette en pointe. As you make your preparations for the turn, pick one spot in front of you. Do not take your eyes from this spot, even as your body moves. This will require turning your head as you move, then whipping it around quickly to the front again, finding the same spot as you begin the second turn. Proper spotting is the only way to complete multiple turns, as you master double pirouettes, and will even help you with other tricky turns, such as the infamous fouetté series in "Swan Lake."