It's been many years since I even handled a S&W Schofield, so this may not be exact.
As I recall, you break open the revolver, then pull on and "unscrew" the cylinder until it comes off.
Further disassembly isn't necessary, or advisable.
Then, you just clean it the same way you do any revolver.
Brush out the chambers and barrel with brush and solvent, then use patches soaked in solvent until every things clean.
Use a toothbrush to scrub thoroughly between the ejector and it's seat in the rear of the cylinder.
Use a lightly soaked patch and the toothbrush to clean off any fouling or firing soot and carbon that you can see.
If you shoot lead bullets, you'll likely need a Brownell's brass chamber cleaning brush to de-lead the cylinder, and a Lewis Lead Remover Kit to de-lead the barrel and the barrel's forcing cone.
The brushes and Lewis Kit is available from Brownell's Gun Smith Supply:
http://www.brownells.com