The inner components are fairly simple, the diaphragm is what usually fails.
If you feel very confident in your abilities to disassemble and reassemble things, you could tackle this on your own; parts are readily available. If you have the slightest doubt though, have it rebuilt, it's not the easiest of things to do.
I had an original booster on my last Dearborn built '65 and appeared to have been painted after assembly, but don't necessarily know if this applies across the board, especially since things varied depending on when and where the car was built.
That's the best I can do on this question. You should be able to look online and find diagrams or photos that detail the inside of your booster and maybe look up any Mustang Monthly Articles online where they performed a rebuild.
Good luck...Ray
