First, never bother a farmer or landowner while he is working or during meal times.
If grade school age, taking a parent along while asking permission will help convince the landowner you are responsible & will respect his land.
Start by telling him you are a trapper & would like to trap raccoons (or whatever you're after).
Other than doing a footline, ASK if you can use a quad, horse, or car to get to your sets.
While scouting before season never walk through planted crop fields. It's a sure way to lose permission.

Great advice, thanks!!

Go ask way before the season and ask to help out around the property. Beg them to help in any way possible. They say no, go back next Saturday and ask them again if you can do anything to help.
If you find a gate open, leave it open.
If you find a gate closed, leave it closed.

Stay off adjoining property unless you have permission. Do not trespass.
Be nice to all the neighbors and ask them if you can help them around their property. Then, after you have done some work, then ask if you can do a little trapping to help them out.
Thank them and stop each year, even if they say no. They might change their mind after talking to their neighbors.

These are things that got me more land to trap and hunt on. I had to watch the back gate for trespassers every opening day. It paid off. They gave me written permission for over 5000 acres of prime Pheasant and dove hunting and as much trapping as I could do. Then I caught a trespasser and warned them, said I was telling my guy. Turned out he was the adjacent land owner and told me to stop at his barn on my way home. He wrote me another permission slip for over 10,000 acres next door.

And with all that the landowner will tell his neighbors, and you can get a good reputation and even better opportunities than just trapping.

Ask them to fish on their property or shed hunt or mushroom hunt or something that is pretty “harmless” then make sure to talk to them about anything you can and make yourself a good reputation. Then politely ask them to trap and most of the time it will go your way.