If you just want to wash their feet, then stand them in a bucket with 2 inches of water with a mild shampoo. THen rinse thoroughly and towel dry. Put fresh shavings in their coop to help absorb any water remaining in their foot feathers and accept that they will get dirty again soon.
If you want to wash the whole bird, such as for show:
Washing:
Use three tubs, or big buckets of warm water.
The first one should have mild shampoo in it. You can use "mane and tail" shampoo, baby shampoo, or even flea and tick shampoo. Put the chicken in it to its chest or neck (hold onto them or put a towel in the bottom so they wont slip and go under) and work the soapy water into the feathers with your fingers. Try really hard to keep the soap out of their eyes and ears. Swish them around a little then take them out. You will get wet.
Next, rinse them in the second bucket which should have warm water with a little vinegar in it. That is to get all the soap out of their feathers. Take them out. You will be very wet by now.
Last, rinse them again in clear water. If they are white birds, you can add a couple drops of Mrs. Wrights Bluing to the water to brighten up the white. Notice that I said "a couple drops". More is not better. More is a blue bird. LOL
Drying:
Wrap the bird in a towel and set it near a heat lamp (unless it is a hot day, then eliminate the heat lamp).
While the towel is soaking up the excess water, you can start the next bird.
By the time you finish the second bird, the first bird should be ready to place in a dog crate/small cage/or box with lots of shavings, and kept there overnight. Make sure that they are in a location where they wont get chilled overnight. I bring mine into the house or the garage and put a light on them if needed.
They will take quite a long time to dry down to the skin, overnight at least. You can speed the process up by using a blow dryer, but you must be very careful to keep it on low temperature and not burn the bird's skin.