you'll need a bucket, a sponge, shampoo, conditioner, sweat scrapper.
Optional are a curry comb (or some sort of thing to get the soap down to the skin to get them sparkling)
I would either have your horse tied or have someone holding the horse. If you don't know how to the horse will react to water.
I fill a bucket up with water, and put the shampoo in there.
Then I wet the horse (all the parts I want to bathe, but I don't spray the head)
Then I get the sponge and soap them up.
Then rinse the soap off, then sweat scrape.
And you have a clean horse!