First, harvested yeast will keep for a year. You would have to purchase DME for starters for yeast that old, though.
There are lots of ways to harvest yeast. I use a gallon wine jug. After bottling my beer, I add little more than a gallon of water to the fermenter and swirl up all the gunk at the bottom. Then I let it sit 10 minutes. This allows all the heavy material to fall to the bottom and the lighter, healthy yeast to stay in the liquid. Then I fill up my gallon wine jug with the liquid and put it in the fridge. After about 3 days, when the yeast is nicely settled at the bottom of the jug, I decant most of the liquid and split the yeast into smaller jars. I split up ale yeast into 3 jars and lager yeast into 2. If I’m using the yeast within a month, I just pitch the jar into the batch. Over that and I make a starter. Yeast is a pretty big part of the beer budget but harvesting yeast will save you hundreds. Out of 1 pack of yeast, you can make 121 ales or 31 lagers. I have not gone beyond 5 generations but when I move to all-grain brewing I’ll see how far I can go before the yeast stops doing it’s thing in small 1-2 gallon batches.
