I start from the end that's out (non-tape end) and just let the paper backing fall away as best I can while putting the film on the reel. When I get to the end, I pull the tape off of the paper and fold it over the film end. It's nice to have it there when I'm hanging the film up to dry as it stays in the hanger clip better.
One trick that I read somewhere online was to clip the two leading edge corners of the film just a bit. I tried it and it makes it much easier to start on the clip.