Yep, exactly what Kevin said. Keep in mind, the "Barrel" part of the computer and the actual head with the pricing wheels, etc do not need to come apart. This whole thing comes out as 1 unit.
If it's in decent enough shape, you can clean it up with simple green (awesome degreaser/cleaner) and a stainless or brass brush. Don't use the brush on the wheels though unless you plan on repainting them. Compressed air helps a lot too.
If it's in less than good shape, consider sending it off to Joe Yocum, a member on this site. It will come back looking NEW. There's lots of pictures of Joe's work on this site, it's amazing what he can do with a computer. It sounds like this is your first pump, if it is, I wouldn't even think about trying to disassemble the computer yourself unless you're a mechanical/gearing whiz. I did that once for fun on a busted up computer and needless to say it ended up as a box of parts.