I buy a vial of yeast and make a brew from it.
When it comes time to keg or rack to secondary, I wash the yeast from the primary, and save it for future brews. This easily gives me enough yeast for another 4 brews using second generation yeast.
I also wash the yeast from each of those subsequent 4 brews, each time, collecting enough for yet another 4 brews. So far, that gives me 21 brews (1 + 4 + 16) from the one vial of yeast. If I wanted to (and had room to store it), I could repeat this process again, and get another 64 brews using 3rd generation yeast, but I usually end up by investing in another vial.
I have on occasion used 4th or 5th generation yeast, but I have also noticed that the yeast is mutating by that time, and produces different results to the first generation, so nowadays I never go over 3 generations.
-a.