Choose an object to look at before you take off into a pirouette. Keep your eyes on that object for as long as possible before turning. Spin your head quickly around and find the object with your eyes again. This will help you not become as dizzy in your turns.
Focus on your arm position which should be slightly in front of you, elbows bent and curved, about in line with your stomach. This arm position will help you stay balanced when you are spinning in a pirouette.
Keep your body as vertical and straight as you can when performing a pirouette. Your pelvis needs to be straight and your shoulders need to be as square with your hips as possible. There should be no twisting of the body and it should all move together.