The biggest thing is just to ask. Like others have said, you will hear the word "no", but most people are jerks about it. For a long time I hesitated to ask to hunt private land and relagated myself to public spots. Now I just ask and even if they say no I usually end up having a nice conversation, ect. I never expect anyone to give me permission, but where I'm living now, most people do. I REALLY appreciate it and I make sure I show them by bringing them stuff (carrot cakes, gift cert., goose/duck jerky and pepporoni sticks, ect).
I kinda enjoy asking permission now, it lets you get out and meet some of the hard working landowners nearby and most are great people
Of course...when I lived in the Gallatin Valley and Bitterroot Valleys it was kinda a different story, if they are locals then most are at least pleasant, if they are imports, well, lets just say that unfortunately they often have a different attitude ("this is MY property, I paid for it, why would I let you use it").
Anyway, good luck!