Step 2:
Spray the dry rim with wheel cleaner, available at any auto parts store. Let the chemical sit on the wheel for a while (the cleaner's directions should specify how long). This chemical will eat through the brake dust that has built up on the wheels and make the hand-cleaning easier & faster.

Step 3:
Rinse off the wheel cleaner with medium-pressure spray from a hose. As you rinse, direct the spray toward the ground to keep the potentially abrasive wheel grime from splattering on to the rest of your car. High-pressure is not recommended due to splattering. After this step, most of the grime from your wheels will be gone.

Step 4:
Mix a soap-and-water solution in the bucket, following the directions on the soap. Soak the sponge and use it to clean away any remaining visible grime. When it's time to re-wet the sponge, first rinse it with the hose outside the bucket. This will cut down on the grime that gets into your water/soap solution.

Step 5:
Rinse the soap off the wheel using medium pressure, just like you did to rinse off the wheel cleaner.

Step 6:
Use the soft-bristle toothbrush and soap & water solution to clean any areas you weren't able to reach with the sponge. For example, the area around the tire valve stem may need this. If you have rims with intricate wire-work, you may have a lot of work to do at this step.

Step 7:
Rinse the soap off the wheel using medium pressure, just as before.

Step 8:
After you wash the rest of the car and it's time to dry the rims, use an old cotton towel to dry the rims. The towel will pick up any remaining bits of grime and help you avoid water spots.