Tools & Chemicals:
Dish soap, bucket, soft cloth, sponge, brush & hose.
If the drivetrain is dirty and requires cleaning, clean the drivetrain before the frame.
Using a garden hose or bucket wet down the frame. Do not use spray attachment, it will force water into areas you don’t want it. Wash the bike like you would a car using the cloth for hard to reach areas and the brush for stubborn dirt. Use the hose to rinse off the frame, handlebars etc. again do not use a sprayer just a gentle rinsing action. Dry the frame with a terry towel and apply a wax (car wax will do)this will make future washing easier. To clean the tires use the same technique, washing gives you a good opportunity to inspect for damage and signs of future maintenance concerns.
A good wax to use is a spray type car wax and just spray your clean cloth and wax your frame. Make clean up easier and rinse your bike after you get home from a hard ride in the mud, the extra few minutes will save you 10 times the amount in time if you let the mud cake on.
Wash your bike leaning against a garage wall or some form of solid support to prevent it from falling when washing and causing damage.