Oyster mushrooms typically produce a lot of spores so that part should be OK. Just by leaving the mushrooms on any surface, loosely covered overnight, will result in a spore print (a pattern of spores released). It's fun to leave the caps with stems cut off, gill side down, on different colored paper to see what color spore print results.
However, in order to successfully grow the spores later, you need to sterilize the surface, and make sure it is not still hot if you used heat.
So far, my best uncontaminated spore was collected on a glass Weck canning jar lid, boiled for 15 min along with the jar, then removed and left to cool upside down (the jar on top of the lid). You can also bake an aluminum foil in an oven and some people talk about baking papers. Alcohol and/or hydrogen peroxide can also be used. You need to make sure the spores are thoroughly dry, away from contaminating mold spores, etc. Then they can be stored until ready to use. Thoroughly wash hands (like surgeons you know), DON'T wipe hands on towels, and use rubbing alcohol to sterilize and dry your hands before handling anything.
My last attempt to grow spores on agar, the spore print was made on a black constraction paper that had been sprayed with alcohol, then peroxide. I had one or two spots of mold on the agar, but scooping them out, so far, seems to have been successful. Some details and photo are on the other thread that I linked above.
When I don't make special preparations, and I still end up with a spore print, on a plate, paper towel, or on the cutting board, etc. I get a mixed feeling of frustration that I *could*/*should* have saved the spore properly....
I sometimes save the spore print anyway.
For optimum flavor, these mushrooms should be harvested before the rolled down edges turn up. Time to harvest, Bu88les?