Flars is giving you spot on information. He nor I "wash our yeast" we collect it right out of the buck swirled around with a tad bit of whatever beer was in the bucket just enough to break up the yeast cake and make it pour-able into jars. This then separates on its own in the fridge to about half yeast half beer. We leave that beer on the yeast as protection. The yeast are dorment at this point till you need to wake them up.
Our process may differ from this point as he doesn't elaborate but I bet we are close.
Mine is very simple.
1) I pull my yeast out of the fridge at the start of brewing ( if I dont forget, sometimes I do and start this process with very cold yeast) and just let it sit on the counter and warm up. Beer on top and all just let it sit there.
2) Go about my beer brewing and when I'm collecting my 3rd running's I save 2 to 3 cups of the first pull of that hot wort..it is usually around 1.020 at that point...just perfect for waking up yeast.
3) I let that cool a bit but not all the way as I want the mixed in yeast to be at at least 70 to 80 degrees. So I then take the yeast jar pour off all the beer and slowly add and swirl the hot wort into the yest till it comes up to that 70 to 80 degree temp.. I usually will have at lest 2 to 4 full cups of yest and wort by this point depending on original size of yeast harvest jar, rather it was a pint or a quart.
4) After swirling and shaking a few times to introduce oxygen I just lay a paper towl over the jar or more often just lightly set the lid back on the jar and walk away and go back to other brew duties. This whole process takes maybe 2 min.
5) During the boil I will come back and tighten the lid and give a good shake..then open again to oxygenate some more and just let the lid rest loosely again. I might do this 4 or 5 times in that 60 min boil...by that time 1/2 the time I have yest activity making a small mess on the counter as its overflowing the jar. The yeast have woke up and returned to work propagating themselves again. They are ready to pitch at this point.
An important note here.... Not all my jars will show this much activity all the time..it doesn't matter dont stress!...the yeast are still there still waking up and ready to return to work. I have never had a yeast cake fail to restart, regardless of the precieved activity, and I have used them 4 months old. Longer then that I toss them. I have never had off flavors using old yeast cakes or new ones as long as you dont use a IPA yest cake in a blond or some other light beer. Then you will in my experience taste hints of IPA. Porter or stout it doesn't matter which way you go in my tests.
I always use one full cup of this mixture for each 5 gallons of wort so 2 cups for 10 gallons . I can inoculate 20 gallons of beer from one quart mason jar with my method, from a yeast cake that was only collected from 1 5 gallon batch. That;s a 4 times increase on your 1 package of yest investment. I suppose I could inoculate our normal 30 gallon batches with just the one quart as well and probably would if it was all in just one fermentor but I have not tried stretching it to 6 buckets yet as there is no reason...We have plenty of yeast.
Those 4 buckets once collected will now inoculate 16 buckets!...How much yeast do you need to save?
We usually have active air lock activity within 12 to 18 hours or almost twice as fast as direct pitching dry yest. I dont go more then about 5 generations before tossing and starting with a new package of yeast. I have gone 7 with no appreciable difference in my beer.