Wonderfully helpful posts...
Computational physicists usually do some pencil and paper stuff to figure out how to model something most efficiently on a computer. It's good to know how a computer works almost to the level where software and hardware meet, like memory storage and processing, things like that. At a higher level, you'll want to know a lot of numerical analysis and methods so that you figure out the fastest and/or most accurate way to solve a problem.
In a way, I think computational physics is still like traditional theoretical physics. I spend lots of time with pencil and paper trying to figure out what some equations mean in different ways, and really understanding how these formulas work helps you to figure out better ways of solving problems. Then of course you'll need to know how to program pretty well, and some people don't like that, but I think it's fun and it's something that requires significant brainpower, though it requires a different way of thinking than the way you think about physics [usually].
Your question was sort of vague and general, so I hope that's what you were looking for.