Step 1: Materials
Empty coffee cup(s)
Enough coffee grounds to fill your cups
Oyster mushroom spawn
I'll assume you can manage to scare up some empty coffee cups. Ideally you want the little plastic lid part as well. It will make things simpler.
Coffee grounds are really easy to procure. You're gonna need a decent pile of grounds so the best way to get them is just to head to your local coffee shop with a 5 gallon bucket. Just ask them to throw their grounds into the bucket and tell them you'll pick it up in a day. Starbucks says on their website that they will always give you grounds if you ask. I've had great luck hitting the local indie shops. The people who work in those places tend to be cool with the project. You don't want to get grounds that have been sitting around because that will only increase the likelihood that mold will start to form.
The mushroom spawn is something that you will probably have to buy. I would recommend just buying a block of espresso oyster spawn from Fungi Perfecti here:
Step 2: Put it all together
You're going to be mixing some spawn with the coffee grounds in your coffee cup. You want the grounds to be moist but not wet. The kind of environment you could picture mushrooms liking. I find it easiest to add the grounds I'm going to be using to a bowl and moisten it all at once. It makes it easier to tell if things are too wet.
Fill your coffee cup about 1/3 full of your wet grounds. Then break off some of your mushroom spawn from the block and crumble it up into the cup. You want to add around an equal amount of spawn and mix it with the grounds pretty thoroughly (I find a chopstick works well for this). Then simply fill the cup the rest of the way with moist grounds, pack it down lightly, and replace the plastic sippy top and label the cup with the date.
Step 3: Now forget all about it
When your patience runs out and you check on them you will be able to recognize the first signs of mycelium. It will look like spots of delicate white ropey stuff growing on the grounds (pictures below). If there's no activity just give it more time. Oysters are very forgiving but things may take more of less time based on environmental factors.
Unless you are very lucky you will probably end up having some cups develop spots of green mold. It's a common frustration of mushroom growing. Mostly you are trying to get your mycelium to out-compete the mold because you will never be able to avoid it completely unless you happen to have a clean room. If you do get spots of mold you can try to delay it by filling a spray bottle with hydrogen peroxide and give the mold some sprays. Mycelium is actually very tolerant of peroxide so it makes a good choice for keeping things clean. Just be careful because based on the concentration peroxide can burn the skin.
Step 4: When things go wrong
In my experience the most common issue you will run into trying a project like this is ending up with moldy cups of old coffee grounds instead of tasty mushrooms. I had this happen quite a few times and got a bit frustrated. So when a particular cup got too moldy I would dump the grounds and cup into one of my worm bins that was without worms at the time. I did this with a few cups of grounds and after a month or so I took a peak to check on my worms and was surprised to see lots of mycelium growing.
I poked around a bit and the mushroom spawn definitely seemed pretty happy so I stirred in a little straw to lighten the medium up a little and a couple weeks after that I checked again and found a crazy explosion of growth. The bin was in my basement so was never very warm and definitely stayed very damp. I guess my point here is that mushrooms are very complex organisms and experimenting with growth parameters can definitely have good results.
Step 5: Fruiting your cups
To fruit well at this point your cups need air flow and indirect light. You don't need much light and you really can't have too much air flow. It would also be best to keep them someplace fairly moist. You really don't want the cups to get dry at this point so something to cover them up with to hold in the moisture will help. If you have a plastic seedling box thing or something like that it would probably work well.
Below you can see pictures of some cups with mushrooms starting to fruit. I will post additional pictures as they get bigger but you can see how it's going to work. As a final note I'll say coffee cups seem to work well as containers but I've tried many other materials with mostly good results. For awhile I was filling everything in my house that wasn't nailed down with mushroom spawn. Plastic containers, canning jars, old food containers, you name it. So have fun and experiment to see what works best for you. You can see some pictures of other containers I've tried below.
Step 6: Harvest
This is the fun part. You want to harvest your mushrooms when they're still fairly young and tender. Also before bugs get to them. At this point I have oysters fruiting in all kinds of containers. One big trunk full of coffee grounds produced almost 10 lbs of mushrooms on the first harvest. After one harvest you can let the substrate rest for a week or so then soak it down with water and it should give another flush of fruit. This can be repeated up to 5 times for oysters but 3 is probably more typical.
Also you can see a pick below of a plastic bag that started fruiting oysters out of a little hole. I didn't even innoculate this bag intentionally. It was just a moldy bag of old coffee grounds sitting in my basement that some spores must have found their way into. This illustrates two important things about oysters:
1) They are insanely aggressive! They will eat anything so are really fun beginner mushrooms as all other species are considerably more picky.
2) They drop a TON of spores. This is kind of cool to see but note that breathing in spores can be very bad for you especially if you are fruiting these indoors. Some people have developed very bad allergies as a result of living around oyster spores. If you want to do a bigger grow I would definitely recommend fruiting them outside where fresh air can take the spores away.