Some tips:
Use a brand new razor if you're having trouble. Razors lose a lot of their sharpness on the first few cuts, and having one of the proper sharpness makes a noticable difference in how smoothly this process can go.
Definitely go slow. As painstaking and time consuming as this process can be, it's worth doing right. Obviously.
If you really don't feel comfortable doing this yourself, ask someone else to do it for you, either as a favor or as a professional job. You'll be happier in the long run.