Before you can propagate a yeast, you need to source a yeast. For the majority of us, this involves getting a pack of Wyeast, a vial of White Labs, or may be even a pack of dry yeast. It could also mean that you want to culture a yeast from another beer that's been bottled with live yeast.
For the purpose of this write-up, I will be using Wyeast #1007, that I purchased 2 weeks ago. The package is dated Sep 2011, which I'm happy with.
The first part of the process starts with "smacking the pack". Some will say that this isn't really necessary, but I like doing it, because it gives me the chance to prove that the yeast is indeed alive before we go any further.
I smacked the inner pack by locating in a corner of the pack, and giving it a sharp blow, and I put it on the countertop to let it swell up.
I put the pack aside, and 4 hours later it was already showing some puffing, which I think is quite impressive.
This is at 12 hours. Also in the picture is a 1/2 gallon of wort that I will be using to make the initial starter.
I use a growler to do my initial propagation when I use a new yeast. So I filled up my growler to the brim with a solution of water + sanitizer. I'm going to let it sit for a while, which depends on the contact time of the sanitizing solution.
Once the growler has been sanitized, I empty about 90% of it.
I then fill it about 1/2 way up with tap water to give it a rinse. The remaining 10% of the original solution, mixed with water, give me a very light solution of sanitizing fluid that I consider to be safe. Once drained, the minor remnants of sanitizer (a few droplets of very light concentration) will not damage the yeast cells once I fill the growler with the volume of wort that I will inoculate.
I cover this with a square of aluminum foil. (I don't sanitize it, but it wouldn't hurt) until I'm ready to fill the growler.
For the starter medium, I like to use a "near beer" of about 1.030 to 1.040. I do not use hops in that wort, but some people do. I've never really found the need for it. In my example here, I'm using a 1/2 gallon of wort that I made a while back, that I pressure cooked at 15PSI for 20 minutes.
The quantity of LME/DME required for a 1/2-gallon starter wort is approximately 6oz (weight) of DME, or 8 oz (weight) of liquid malt extract. This will get me right in the 1.030 to 1.040 range. This does not need to be super precise, it could even be 1.050 and it would be fine.
Since not everyone has access to a pressure cooker, the general idea would be to boil some water, add DME or LME, boil for 10 minutes, and chill the wort down to about 70F. Since the volume of the growler is 1/2 gallon, chilling that amount isn't too hard with an ice water bath. I will revisit this section on what needs to be done to ensure that the starter wort remains sanitized (near-sterile).
Before transferring the wort to the growler, I prepare a bowl with sanitizing solution, in which I put my scissors that I will used to cut the Wyeast pack, an airlock and rubber stopper, and the unopened Wyeast pack itself [One never knows what's living on the side of the wyeast packs!]
Since my wort has been in a mason jar, I consider the contents to be sterile (provided the lid is still under vacuum). However, I do consider the edge of the mason jar (once the band and lid are removed) to not be sterile. As such, I use a small propane torch to heat up the side of the mason jar. I try to turn it around somewhat rapidly to prevent overheating and cracking the glass. I also do the same for the growler. I believe the growler glass is less heat-tolerant than the mason jars so I'm super-careful when flaming the neck (and it's also smaller so it takes less time).
Once the contents of the mason jar is inside the growler, I again put a piece of foil, until I am ready to pour the contents of the Wyeast smack pack into the growler.
Once I've had the wyeast pack and instruments in the sanitizing solution for the prescribed amount of time, I will grab the scissors, the wyeast pack, shake the wyeast pack to mix it up, and cut a small corner of the pack, and pour the contents of the pack into the growler, and put the foil back on the top until I assemble the airlock + stopper and put it on.