I try to take my kids with me when I go ask for permission. It's hard for someone to tell you no when you've got an excited 3- and 4-year old with you telling them how they want to go with daddy to shoot a squirrel!
If given the go-ahead to hunt, I am always sure to express my appreciation for permission to use their land. One way I do this is to ask if they enjoy wild meat and tell them that I'd be glad to share anything that I take off of their land. Most aren't interested (or they themselves would be hunting and wouldn't want you there) but I have run into several families that get very excited about the prospects of a mess of squirrels, some backstrap steaks, or a turkey breast. I shot a turkey on a farmer's ground a few years back, and I made good on my offer of sharing. It kinda hurts to part with half of the only turkey of the year, but they were very appreciative and have always let me return. It is definitely worth it.
Another tip... If you are turned down, thank them for their time and don't push the issue. Leave a good impression and it may help you in the future. I got permission this season to hunt a property that I was denied permission on 3 years ago. And 2 of my 3 toms came off of that property!
Always remember when you are on someone else's ground, their rules go, no matter how extreme you may think they are. It's hard to find places to hunt these days so don't ruin your chances in the future!
rw