Good spins are balanced. If you are leaning over or unstable, it will be extraordinarily difficult to spin without falling over. Thus, balance and centering are essential skills for successful spins.
There are lots of drills you can do to improve your balance. These drills are generally variations on the theme of standing on one foot. You can increase the difficulty level by closing your eyes or by standing on an unstable surface (like a trampoline), but the core principle remains the same: remain in a balanced position when you only have a single point of support.
Balance becomes easier when you can control your center by stabilizing your core. A tight core helps keep your body moving as a unit; this in turn makes balancing easier because you can focus on balancing a single point rather than flailing all of your extremities.
To improve your centering, stand with good posture—head up, shoulders back and down rather than slouched forward and raised towards your ears. Engage your core by thinking about zipping up your muscles from the hips to the ribcage; this should create a lifted feeling in your center. The combination of good posture and zipping up the core will dramatically increase your stability.
The Drill: With good posture and a solid core, stand on one foot for 30 seconds. Switch feet and repeat. If that is easy, try closing your eyes while standing on one foot.
Repeat this exercise throughout your day. When you are riding an elevator, do so on one foot. While you are brushing your teeth or washing the dishes, stand on one foot. Frequent repetition is the key to this drill!