Permission to hunt...from a complete stranger...in todays environment you have your work cut out for you. That said, give it a try.
Go at a reasonable time of day when you expect them to be home, but hopefully not sitting down for a meal. If you don't already know it, find out the name of the land owner before you go and introduce yourself to them by name; "hello Mr. Smith, my name is .... and if I could I'd like to take a minute of your time to talk to you about the possibility of hunting your property this season." Explain that you're a responsible individual who has completed hunter education/safety (hopefully you have) and that in exchange for his permission to hunt that you'd GLADLY return to the property and help him out with whatever chores need to be done to help maintain the property. Offer to share some of the deer meat with him as well.
Obviously a key factor is being polite and looking the man in the eye and speak with confidence. Don't show up in shorts, a tank top and flip flops with a can of coke in your hand. I know this sounds like a silly thing to say, but it's happened to me with someone asking permission to hunt land that I manage (don't own).
It's a hard gig now days. 25 years ago farmers in Missouri (at least in my area) would let folks hunt just for the asking...even strangers. Today a lot of farmers make a business out of it by leasing the land to clubs and it can be really hard to get your foot in the door.
Don't give up. If one says no, go look for another. A lot of it has to do with who you know and if a friend of a friend can help...don't overlook that option.
Best of luck to you.
By the way...the piece of property that I mentioned managing...I don't get paid for that. I fell into the job by finding out who owned the land, meeting them, thankfully getting permission to hunt and by taking good care of the property for them. That led to me having full authority over the property and who does...or does not hunt it. Win-win for me and the land owner.