Island Paintball has a great reball facility that is (I believe) only $30 for unlimited reball. They're really laid back, so if you know the layout for the next tournament you'll be playing, you can set up the bunkers to model the field layout and run the drills Laxplaya88 suggested.
Also, Cousins Paintball runs the Cousins Tournament Series (CTS) in Riverhead which is one of the most popular series in New York, and there's always teams practicing on Sunday's there. You can also contact other team captains and ask if they'd like to scrimmage. Playing other real teams is the best way to get the most experience quickly, in my opinion. Drilling comes in handy later to perfect and fine-tune specific skills.
RIP LI Inferno
No pickles, no onions