Hey danandteri,
I was waiting for someone else that knew a little more to answer you. I'm not an expert on John Denver, but I have played several of his songs. The first thing you want to do, is learn the chords to the songs. I've played most of his stuff with a flat pick, but I think he was more of a finger picker.

Start with something simple like "Sunshine" and then "Country Roads" would be a good one. That was actually the first song I learned on guitar, and I still remember it.

Let me know a little more about what you're hoping to accomplish, and maybe I can be more helpful.