All salsa dancers start off by getting dizzy once the turns are taught. But, once you are passed that beginner's phase, I am sure you start wanting more and more spins and turns. This applies to both follows and leads.
Here is a really good exercise to practice your spin technique. This is actually the same exercise I did when I was learning how to spin.
Spinning Technique and Tips:
1. Keep a strong core. This means, keep your abs tight as it helps create a strong hold between your upper and lower body.
2. Do no over rotate your shoulders. Once you start spinning, your body should be in plane field - just as if you were standing straight.
3. Keep your legs firm and together. Keeping your legs together helps keep the center of gravity close to the center and will make you less wobbly.
4. Use your shoulders and arms to start the spin but keep in mind point number 2.
5. Spot. Spotting will help you avoid getting dizzy - keep an eye on one spot.
Another spinning video:
Once you have mastered the spinning technique it will help you throughout the dance and enhance your moves on the dance floor.