To spore print a mushroom you will need:
A pair of cuticle scissors
A few small glass drinking vessels or shot glasses
A piece of thick paper like white construction paper, cut into a square a bit larger than the cap of the mushroom one wishes to print
Hydrogen peroxide
A sewing needle
A flat, nonporous surface and a glass vessel to cover the surface, such as an upside down cup on a plate. Make sure it is large enough to fit a mushroom cap and the piece of paper inside with plenty of room.
You soak all the metal implements in peroxide in the shot glasses for a few minutes. Get everything together, then stick a pin into the cap of the mushroom you want to print. Place the paper onto the nonporous surface. Snip off the cap as close to the stem as you can while holding the pin, and in a smooth motion place the cap onto the paper, and cover the whole thing with the cover. In two days, take the cover off and use the pin to lift the cap from the paper.
This probably isn't suitable for reproductive purposes, but the porous paper holds the spores so that you can use them to identify the species. Taking into account the physical description of the mushroom, and the color of the spores, one can be fairly confident in identifying what one has picked.