Hello hello! If you're new to airbrushing, then the simplest advice is to get better aquainted with your brush. Just curious, what model brush did you get? The easiest solution to avoiding paint buildup that I can think of is to simply spray less paint. Again, the ability to do this will come the more you use your brush, but for now, just remember to always keep the brush moving, and to do so smoothly! If you go too fast, the paint won't go where you want. If you go too slow, you'll get the buildup that you're hoping to avoid. Also, be sure your brush is always perpendicular to the surface you want to paint (at least for painting large sections like a hull or wings)...the hull most likely won't be completely flat, so take into account the angle you're spraying at. It's entirely possible that you're actually spraying a bit under the tape. Which leads me to my next point: make sure the tape is well burnished before painting! (Also if you're taping over a previously painted section, be sure the tape is firm enough to hold but weak enough that it won't strip the paint when you SLOWLY AND CAREFULLY peel it back!) So recap time:
1. Keep the brush moving smoothly across the target;
2. Keep the brush perpendicular to the target;
3. Burnish your quality (Tamiya) tape well before spraying;
4. Practice!!! And the best way to do so is to keep building models!  
 
 Hope this helps you in your modeling adventures. I remember when I first used my airbrush...a bit intimidating, but the results are unbelievable! Best of luck, my friend!