There's also the part of what you need to do after obtaining permission. You should pass along your thanks at seasons end, possibly a written letter of thanks, a hand shake and verbal thanks, or even so much as a gesture of some sort. The owners of my trapping properties receive walleye fillets when I get onto some feeding fish. Perhaps it is an offer to help out with any choirs of sorts throughout the year. As well, the seasonal problems they may encounter with non furbearer type critters that cause a problem.....gophers, squirrels, etc.....offer to remain available to help them out should they need something trapped during the off season. Lastly...stay in touch. Don't simply approach them each year right before season. treat them as a friend, and the relationship will grow. Feel them out....some farmers would prefer a daily update, as they may well be as interested in your progress as anyone. Some, on the other hand, would sooner go about their business, and leave you alone. Understand who is who, and what they expect as far as communication. Be clear on your limits.....can you drive the fields or not. Like Tom said....eventualy folks will seek you out. Word on the street is a powerful tool, and being responsible (both to their land, and in your efforts), efficient, good mannered, and law abiding...you will establish a network of folks that will have you being the "go to" guy for trapping. It works, I have folks calling me and identifing themselves, for example, as "the guy that owns 200 acres next to a property you allready trap", "Roger says I should give you a call to get on my land too". Gotta love it when the word of mouth spreads in a positive light. It's up to you to walk the walk.
Good luck!