To wash yeast you'll require phosphoric acid and either a pH meter or pH strips. The general idea is to add acid until the pH drops into the 2.1-2.3 range and hold for ~30 minutes. At that pH, bacteria will soon perish but yeast will survive a bit longer - at least the healthier cells will. Breweries will wash their yeast just before repitching (about half an hour before) as even the yeast cells will die eventually at that pH.
To do it, you generally take say 1l of thick yeast slurry in a 2-3l glass vessel (which will be unaffected by acid). Premix a small amount of acid with water in a different vessel as this diluted acid solution is more "forgiving" than trying to add acid a few drops at a time. Add some acid, test pH. Repeat until the pH falls into the 2.1-2.3 range. Allow it to sit for roughly half an hour, then pitch into fresh wort. I've pitched the whole works before and I know of some microbreweries that do the same; other people prefer to decant the liquid and leave behind the sludge.
I reuse all my yeast 3x - initial pitch from a starter, and then 2 more pitches onto the yeast cake. No infection issues or anything like that, but I'm really anal about my sanitation regime. The microbreweries I'm familiar with will repitch up to 50-60 generations with yeast washing every 5th repitch or so. They all grow cultures from each batch to see if there are any bacterial colonies - if there are, they don't harvest yeast from that batch.
