My method for yeast propogation is as follows:
-On brew day, after the wort in the kettle is cooled, transfer 10% of the wort to a small fermentor, and the remaining wort to the main fermentor, without aeration.
-Pitch your yeast into the small container, the kräusen starter. The pitch rate is up to you; I generally pitch half of the recommended amount of yeast for the batch size ie 1 vial.
-Shake the starter to aerate, and allow it to ferment. Again, fermentation temperature is up to you. I generally leave it at room temperature until fermentation activity is evident, then allow it to cool to the desired pitching temperature (anywhere from 6c-9c for lagers, depending on strain.)
-When the starter reaches high kräusen, aerate the main batch and pitch the entire starter into the main batch. This is normally somewhere between 12 and 24 hours after making the starter, strain vigor dependent, of course.
-Ferment as normal.
This method has given me excellent fermentation performance, and is much more similar to the pitching methods of commercial breweries than simply pitching multiple packages of dormant yeast or building and stirred starter and crashing the yeast into dormancy before pitching.
The key difference between this and other methods is that you are pitching HEALTHY, ACTIVE yeast cells that have grown, adapted, and reproduced in the exact same wort that they will ferment upon pitching the main batch, and were not temperature-shocked into dormancy before pitching. For me, this method has resulted in faster, more reliable starts to fermentation, and higher attenuation, on average, all other factors being equal.
Give it a try; as I eluded to previously, there are countless variations that could be made, some of them being starter size, starter pitch rate, fermentation temperature, fermentation duration before pitching, etc. Another thing I like about this method is it gives more than enough time for the main batch to precipitate a large majority of the cold break and any trub that made it to the fermentor, which can then be removed by racking (or dumping, if you’re lucky enough to own a conical.)
Good luck, and happy brewing!