As I look over my work, I think there is no single answer -- other than perhaps I approach things intuitively. It could be an overall shape, alone or relating to other elements in the frame. It might be a line or curve or group of curves. Maybe an odd perspective such as looking upward into starkly lit branches. I have often been attracted by sycamores with their flaky bark patches, especially highlighted against a deep autumn sky when the trees are bare.
Sometimes it's about texture. A few years back I took a shot of sycamore tree bark trying out my Bronica macro lens. I got in close and captured about a 12 inch square section of tree trunk (it's in my gallery stuff here). I entered it in an art show under the title "Sycamore." It got a modest award from a judge who is a painter and quite outspoken about believing paintings and photographs shouldn't mix in shows. But in her judge's comments she left "What a creative approach to photographing a tree! Only an artist would pick up on the design offered by nature." One of those "gee, did I do that?" moments! It later sold out of another show. Was it carefully planned, no, just happened the lighting on the nearby tree caught my eye as I was sitting in my car finishing a cup of coffee before going for a walk with the camera. The shot was selected from several taken that morning, but I can't recall any formal process to the one picked -- just that "I liked it best."
Sorry -- a lot of blather to say "go with your gut instinct."