With that said, be polite, and respectful, dress nicely, offer info like truck tag or cell # so the landowner can get in touch with you if there is a problem. Offer to "keep an eye" on their property for them. Expect to knock on a lot of doors to get that one honey hole, and good luck!
Lots of good advice there. I'll add; try not to show up at mealtimes and don't wear camo. At that point, you're a salesman, and you're selling yourself. I make up index cards with my personal info as well as my truck info, and give it to the person regardless whether I get permission or not. Tell them you would be willing to help out with some chores if needed, (and then make sure you DO). If you have any permissions from anybody else nearby, make sure you "name-drop" a little. Even though the landowner doesn't know anything about you, he knows and USUALLY respects his neighbors, so the fact that one of them trust you might swing things your way. Make sure to stress how much you are a law abiding, respectful hunter, but don't blow your own horn and tell them how many deer you kill and how great you are.
If you get turned down, continue to be polite and leave your card with them, asking that they give you a call if they change their mind after thinking about it. You might think that's a waste of time, but it's not.
If you DO get permission, make sure to keep on your promise to help out. DON'T wait for him to call, just stop by occasionally and see if he's doing something you can help with and jump right in. Treat his property as if it's your own. Either during the season, after the season, or both, make sure to drop in with a gift of some sort. Restaurant, grocery, or gas certificates are always good, venison products will never get turned down, maybe a turkey or ham from a local market. If you really wanna impress, have some flowers sent to the wife. Make sure to include a note so they know who it's from, and thank them for the privilege of hunting his land.