If you haven't already, I also **highly** recommend the book 'Yeast' by Chris White and Jamil Zainasheff, especially if you don't have any laboratory experience.
Step 1: Obtain materials
You will also need the raw materials that will make the solid culture medium. You can obtain laboratory-grade materials from Amazon, or you can make your own 1.040 wort and use yeast nutrient and agar-agar to solidify the plates. You can buy D-(+)-Maltose, Peptone, yeast extract, and agar technical (solidifying agent) on Amazon, believe it or not (autoclave the maltose separately to prevent caramelization of the sugar). While this method produces solid growth medium that is perfect for keeping yeast in a laboratory setting, many folks don't want to shell out the dough for these materials, and prefer to make use of beer-making equipment and materials they might have at home already.
The easy way to do this is to get agar-agar (solidifying agent similar to gelatin) online or at an Asian food store. Then, make a simple 1.040 gravity wort using only brewer's 2-row base malt, add yeast nutrient and 20 grams of agar-agar into 1 liter of culture liquid (can be scaled down accordingly depending on your needs), and autoclave in an appropriately-sized Erlenmeyer flask (you don't want to exceed about 50% of the volume of the flask when autoclaving). Personally, I don't have a pressure cooker capable of autoclaving my 2 liter Erlenmeyers upright and full of liquid, so I make small batches. You can easily make up 1.040 wort and split into several batches (in mason jars) for autoclaving purposes, and these will keep in the fridge or basement as long as they are sealed. Then, you can use this liquid for starters or 50-100 mL at a time for making solid culture medium plates such as we are discussing. In this case, you would take 50 mL of this nice pre-autoclaved wort and add 1 gram of agar-agar to it, dissolve, and autoclave again in an Erlenmeyer flask in your pressure cooker.
Step 2: Surface clean and autoclave your glass petri dishes
Step 3: Drink a Michigan-made craft beer while you wait!
Step 4: Make wort, dissolve powders, and autoclave liquids
Please remember that proper maintenance of your pressure cooker is essential. Read up on the manual for your model and please follow all safety precautions indicated there. A pressure cooker is not a medical sterilization device. Spore test your autoclave after 10 hours of run time to ensure it is sterilizing effectively. A 3M Attest biological indicator capsule is very easy to use. Safety first, people.
Step 5: Setup a semblance of a sterile environment to pour your plates in
I like to keep the alcohol lamp(s) lit and between me and the plates I'm pouring. This acts to catch any stray particulates emanating from my breath or circulating around the disturbed air around my person. While the lid of the petri dish is off, you always want a lit alcohol lamp nearby creating an updraft which will give it protection from a majority of airborne contaminants which would love to encounter this rich growth medium.
PLEASE NOTE: working in proximity to FLAME and FUEL (denatured alcohol) can be dangerous. You are responsible for your own safety. I recommend practicing the motions beforehand, without the lamps lit. Good sterile technique can take years to master, so don't become discouraged. I can't go over all of this since it would require much more than an Instructable, but I think we can reach a good level with common sense. Sterilization is different than sanitization, and anything (upstream or downstream) that comes into contact with these plates will grow on it, whether it be bacteria, mold, non-saccharomyces yeast, or the desired brewer's S. cerevisiae yeast). Just try to be cognizant of the fact that this is GROWTH media. Any small amount of contamination will lead to growth of that contamination, so mistakes can be easily amplified (since we are actually attempting to amplify/grow organisms). If at first you don't succeed, LEARN FROM YOUR MISTAKE, and then try again.
Step 6: Pour plates/slant(s)
When you are done, leave the lid slightly off of the plate. This will allow the heat to escape as the agar solidifies, and you won't get a crazy amount of condensation containing contaminants on the inner surface of your petri dish lid. ALWAYS have a lit alcohol lamp very close by while the lid is off, even slightly.
For my slant, I like to put the foil lid back on while it is cooling, and recycle nearby foil from the plates into a makeshift holder, which allows you to set a custom angle for your slants while they solidify. This means you can use any size slant tube that you might be able to find. Keep the screw top lid wrapped in foil, and put it on later after the slant has cooled and solidified.
Step 7: Cover and store plates
At home, I like to pour a small amount of denatured alcohol on a paper towel and wipe out the interior of a plastic sandwich bag, and store the plates unwrapped inside of that. Once my slant cools completely I'll add the sterilized screw lid to that. These can be stored at room temperature, or inside the fridge. Each method has its own advantages (the cool temp inside the fridge will inhibit growth of any potential contaminants and prevent them from drying out as quickly, although storage at room temperature will fairly quickly alert you to the growth of any potential contaminants. It's a give and take situation). Before you use a plate for culturing purposes, you always want to bring it out of the fridge and let it come to room temperature before you plate the yeast dregs, giving the yeast a bit of a nice warm environment to grow on and preventing a sudden temperature shock.