The best way and Cheapest way
Best way :
Buy brake parts cleaner, it's like an injector / carburetor cleaner but specialized for brake parts.
Brand : Prestone, WD-40, etc (check amazon "brake cleaner")
Cheapest way :
Use gasoline, i'm not kidding you or joking, this is my knowledge from working with my father and several mechanic in my country. although is dangerous for inhaling a gasoline gas this is the cheapest way and pretty much works.
Gasoline will vapourized quickly it will leaves you a clean and dry parts (but pretty much is smell like gasoline).
Don't working with gasoline in closed area (no ventilation) you will get dizzy and high (if inhale too much) and dangerous working with cigarette on mouth
How to use it :
-pour gasoline in place like cup or bowl
-use brush, dip your brush in gasoline, and wash your parts with it.
-if the grease too much, pour gasoline into a bigger bowl that fit your parts, dip it and brush that grease.
Rubbing alcohol will NOT cleaning grease, it just make it worse because swiping movements will leave your parts more greasy
Gasoline is good for cleaning "rubber adhesive" trace too.
edit : after you done clean it with gasoline, leave it until completely dry, you can quickening it with a fan or under the sun.