There are lots of things you can do and I am not sure anyone has the total answer.
As I land owner I am kind of leery of people who show up a week before and ask permission. I figure if they are serious hunters they would want to scout the land early, know where the property lines are, etc. When I am looking for a piece to hunt I make up an index card with contact information including vehicles and license plate numbers. I dress decently and act respectful. If it is an active farm I don’t show up at meal time or milking time and never show up Sunday morning (people go to church). I tell the owner that I grew up on a farm and will respect his property. I ensure him that we will abide by his rules and won’t break his fences down, leave gates open, shoot towards buildings, leave trash in the woods, etc. If possible I bring my two boys with me, introduce them and tell the farmer we are hunting family and were brought up to be good hunters who abide by the game laws and respect other people’s property, including his neighbors. Typically after getting permission I find out who the neighbors are and give them a call just to let them know I will be hunting the property and will respect their borders. BTW- I have three adjacent pieces I hunt now because the neighbors of the original piece I hunt were impressed that someone would be courteous enough to do that so they allowed me to hunt their too. I have hunted a few pieces of property for a number of years and have always kept myself in the good graces of the owners, enough so that a couple of them are now willing to give me a good reference if an another owner wants to call about my getting permission – that is invaluable if you can manage to get someone to do it for you. If you want to find and keep a good hunting spot there is more to it that just getting permission though. Once I find a spot I go the extra mile. I do things like offer to keep an eye on the property, replace posted signs or post the property for them if they want. If I find a broken down fence, I prop it up temporarily and then tell the farmer about it, even offering to go back in and fix it (since I know exactly where it is). My buddy in the Syracuse area has life time permission to hunt this really nice farm because he offered to give the farmer 2-weekends a year in the spring to help fix fences before the cows are let out.