I want to first say that I never disassemble a lock for cleaning. I dunk it in hot water, scrub with an old toothbrush, and spray with WD-40. There's just no need to take it apart. Even with the proper tools there is always a risk of spring breakage or a screw getting cross-threaded on reassembly. I may take a lock apart when I first get it if it looks like it would benefit from having it's contact surfaces polished, needs tuning or, of course, if something breaks. A case in point is the L&R Queen Anne lock on my latest smoothbore. Everything works as it should and there's nothing I could do to make it work better than it already does so why risk taking it apart?
Now, having said all that, it sounds like you have the right ideas and approach to disassembly. Be sure you have the right tools and that includes gunsmith screwdrivers. Study the parts of the lock and how they all work together. There's really not that much to look at. Be extremely careful when removing those springs. Use Bigsmoke's tip and don't compress more than necessary. Be especially careful that the spring doesn't escape the vise and fly away. V-springs are made to work within a limited range of motion and always against resistance to slow them down. A spring which escapes will open violently beyond its intended range of motion and this often results in a broken spring. If there's a fly in the tumbler keep a close eye on it. It is tiny and if it comes free and drops to the floor you will find yourself in the gunsmith version of "assuming the position". That is being down on all fours crawling around looking for it. As you remove springs/screws/parts lay them out in order on the bench. I keep screws next to the part they go with. Assembly is literally in reverse order. Be just as careful putting the springs back as you were in taking them out and be sure to not cross-thread any screws. Piece of cake!
Storm