It is not hard to make a reasonable quality spore print. You need cheap latex (or nitrile) gloves, bio-ethanol (or any other desinfectant grade concentrated alcohol), a few plastic food containers or glass jars with lids, a sharp knife, scissors, tweezers, zip-loc bags ("weed baggies" ), a roll of aluminium foil and a roll of kitchen towel paper.
The zip-col bags, aluminium foil roll and the kitchen towel paper roll should ideally be fresh from the shop, so they'll be "factory sterile" (ie. not truly sterile, but with very little contamination).
Put on the latex gloves, wipe your hands with an ethanol soaked paper towel. Clean the alcohol bottle the same way. Clean the work surface in the same way.
Next, clean the plastic containers or the glass jars and their lids with an alcohol soaked paper towel and put the upside down containers/jars and their lids on a fresh paper towel on the clean work surface to let any remains of alcohol evaporate. Now clean the scissors and the knife with an alcohol soaked paper towel.
With all equipment cleaned, wipe your gloved hands again with an alcohol soaked paper towel and cut a rectangle from the aluminium foil. Place the rectangle on top of an upside down lid and place the plastic container or glass jar on top of it. Having the containers upside down like that makes it easier to manipulate the print and the mushroom cap. You can optionally make a stack of two or three pieces of aluminium foil, in case you manage to make more than one print from a single mushroom cap.
When you have prepared all the containers/jars, you can start putting the mushroom caps in. Place the mushroom on its cap on a clean paper towel and cut the stem where it meets the cap. Lift a container or jar from the lid and put the mushroom cap on the aluminium square, with the gills facing the aluminium foil. Put the container/jar back in place.
Wipe the knife with a fresh alcohol soaked paper towel and process the next mushroom, until you run out of mushrooms or out of containers.
After anywhere between 6 hours or a day, the mushroom cap will have dropped a load of spores onto the aluminium foil and you can collect the print.
Put on clean gloves, repeat the cleaning procedure as above for the gloves, the alcohol bottle, the work surface, the knife and the tweezers. Put a clean paper towel on the work surface.
Gently lift the first jar or container and place it besides the lid. Pick up the mushroom cap with one hand and pick up the aluminium foil square with the clean tweezers. Put the foil onto the fresh paper towel while still holding it with the tweezers. Press the clean knife blade gently down the middle of the foil so that it starts to fold a little. Using the tweezers, fold the foil in half, with the spore print on the inside of the fold. Press the outside of the folded foil a little with the knife, making sure the foil is folded flat. Now open the zip-loc bag and place the folded foil inside the bag and close the bag. Using a marker pen, write the name of the mushroom on the outside of the bag.
Repeat for all prints, cleaning the tweezers and the knife with an alcohol soaked paper towel each time.
Executing this procedure meticulously does not guarantee sterility, which is impossible with wild mushrooms anyway, but it will minimize unnecessary contamination. Spore prints produced in this way are a very good staring point for culturing on agar medium in petri dishes.
Last year I grew an agar culture from such a print. After a few transfers of selected best sections of the agar plates, I inoculated some mix of bran and sawdust with the agar plates. This was then spawned onto a big bucket full of pasteurized wood chips (I had been pasteurizing manure enriched straw and tossed the wood chips in the used pasteurization soup and let is soak a bit). I got a small harvest already last fall. The plastic bucket has stood outside in the shade all winter and summer, I have watered it a few times during the hottest weeks of summer. This fall I expect a really good flush.
BTW, I did try to inoculate cardboard with a piece of stem and some mycelium stuck to it last fall, after I cut the caps to make prints, but I find it to be a bit more tricky than it sounds. The cardboard dries out easily or, if kept too wet, is prone to some molds.