I generally get land by asking if I can hunt the preds and varmints. After a year or two hunting them, I then ask about deer and turkey. By then they know me, I have saved some livestock from yotes and farm equipment from GHog pits, and they have entrusted me.
However, I have gotten permission to hunt some game species right off the bat. A good tactic that has worked for me is to walk right up to them when they are harvesting there crops. I have always had good luck with them wanting to take a break and talk for a few. I've gotten some good land that way. Also, try and look at platt map books. Go to the index and see which land owners in your area have the biggest tracts of land. You just might get lucky and get access to hundreds if not thousands of acres by knocking on one door.