I like this product called: Aqua Glycolic Shampoo & Body Cleanser. It's pretty gentle. But you have to order it online. Usually costs $9 for 8 oz.
Whatever you do don't try mayonaise or apple cider vinegar.
I have also heard about Zinc Soap Bars (are good for maintance to prevent flare-ups) and a brand called Carmol (they make a shampoo which is supposed to kill the yeast that causes the psoriasis flare-ups) to be good as well. I think you have to order these as well. I found a really good site that has all sorts of beauty products. But if you do a search you will probably find it. Sorry I could not post it.