The basics of classical ballet technique need to be thoroughly understood to build strength for pirouettes, and later for ballet classes in pointe shoes. Knowing the finer details of your daily routines gives you an extra advantage to the use of your core muscles in stabilizing your ballet positions and movements.
First a quick review of some basics that will help you make progress toward pointe work, good pirouettes and doing well dancing the kind of roles in ballet recitals you would like:
1. Is your postural plumb line correct in your fifth position standing with straight legs?
2. Do you maintain your postural plumb line and turn out when you demi plie in fifth or fourth position?
3. Do you have a relaxed neck for good spotting?
4. Do you maintain the placement of your hips in your retire position?
5. Can you releve straight up and balance there?
6. Can you keep the foot muscles engaged when you descend back to your landing position so that you land softly into a controlled demi plie?
If any of the above are non-existent or weak, pick the most basic and do a practice routine to correct it. Ask your teacher or a class buddy to help you until it is 100% correct.
If you tip to either side when you releve, check to see if your core muscles are not holding, or if loss of turnout on one side tips you. Also check to see if your arms are closing too forcefully and knocking you off balance.
Doing a series of quarter, half, then whole turns (once you've corrected the basics) without any arms at all gives you the right feeling for more effortless pirouettes. Put your hands on your shoulders or hips and just turn from the force of pushing up out of the demi plie and the working leg turning out as you place it into retire and begin the turn. You'll get around.
For pirouettes en dedans, you've got the force of the working leg pushing off and coming up to retire and the supporting leg turning out as you start the turn, to get around at least once with no arms needed.
The other issue is hopping towards the end of a turn, or throughout. If this happens, try getting a feeling of pushing down through the supporting leg into the floor as you pull up your core muscles and leg muscles. Connect with the floor, even get an idea of drilling down into the floor - use the image to keep you grounded. And check all your basics to see what you are compensating for.
This should help you in how to improve the basics of classical ballet technique for pirouettes. Enjoy! They're fun.
Go here for info on how to prepare for pointe and improve your pirouettes!