This is easier said than done but with reasonable care, luck and modest investment, can be accomplished by the serious home brewer.
A sample from one of these typical colonies is transferred to a test tube containing a growth medium. When this colony is actively growing, it is considered a pure culture and can be refrigerated for later use or started by covering with beer wort. When this starter is actively fermenting, it is poured into a larger amount of wort which, when active, is pitched into the beer.
The first assumption is that one can select the desired strain by looking at colonies on a petri dish. This is more or less true because the overwhelming majority will be the same, i.e. the dominant strain. Bacteria, molds and many wild yeasts are obvious and recognizable to the naked eye.
The second assumption is that, while still very small, all round colonies are the progeny of single cells.
The third assumption is that all such colonies, at least in the center are mono clonal or at least mono-cultures and otherwise sterile.
To do the job right, one would have to study the original diluted culture under high magnification and do a presort at that level. This is revealing and fun. It also gives an indication of any bacterial contamination in the culture but the rub is marking individual cells and finding them later when they grow into colonies. This is done using a calibrated X-Y stage on the microscope and making careful notes. Fortunately, however, I do not believe that it is really necessary for the home brewer, although a must for the lab selling selected strains.
It should be noted that a pressure cooker is the preferred method of sterilization but for our purposes, one could probably get by with steaming in any pot with a lid and a half inch of water. Set the dishes or slants in or on a cup or some other support to keep them out of the water.
The petri dishes are turned upside down after solidifying and cultured this way to prevent water of condensation from falling on the medium. The test tubes are cooled on a slant to allow the water to settle on the bottom when vertical. They are also stuffed with cotton before going into the pc. You can also use tubes with plastic screwcaps and avoid the cotton.
It should be noted that gelatin melts around 75 F so its use in summer is precarious. The better alternative to gelatin is agar agar. This is available at oriental food stores in stick form. Half a stick (about 4 inches) in a cup of wort will get you through the hottest weather.
Flame your wire again and after cooling, remove a small sample from the center of the selected colony and poke this into the surface of the medium in a "slant" test tube. You can do this to several slants, with the same sample, to assure all slants are the same or flame the wire and take a new sample from a different colony. You can make as many slants as you will need for several months and throw away the petri culture.
You now "incubate" the slants until 25% or more of the surface is covered with the pure colony and then refrigerate them till needed.
This process can be used on anything from a packet of Red Star to a bottle of your favorite beer and will produce a pure culture. There is no guarantee however, that the strain will remain the same for ever because of natural mutation. As it is my experience that the most common and objectionable contaminants of dry yeast are bacteria and mold, this process will guarantee at least, to eliminate these most serious problems.
This procedure skips the petri dish part and assumes one is starting with a packet of liquid yeast or a culture slant obtained from a reliable source.
After preparing the agar/wort medium and a convenient number of slant culture tubes, they are simply inoculated directly from the culture.
Using the sterile procedure outlined above, just dip into the packet of liquid yeast with the transfer wire and poke this into the agar in the sterile slants. One dip is enough to inoculate several tubes. You can use the rest of the yeast in the packet to start the next batch but the slants can be saved for a year or more.
If you use a purchased culture slant, the same procedure applies. Poke the wire into the yeast culture and then poke this into the slants. Save the original for future iterations. If you started with a liquid yeast packet, save the last slant to start a new group.
Using this simple approach, one can go several years without spending a penny on yeast and possibly forever once you get into the "yeast swapping" mode. I have yet to buy any yeast since I stopped using dry.
While this is not necessarily music to the ears of yeast suppliers, it is good news to the homebrewer. That $'s for yeast in the bill of materials becomes zero to the yeast culturer. Yeast suppliers (like extract suppliers) will no doubt always be with us and in the case of yeast, we need them to maintain pure strains when ours go south. But to keep buying the stuff for routine use is strictly for the affluent and laz.... naw, I won't do that again.