Don't know about damp paper. It can take months to get adult ferns from spores. To collect spores I usually take part of a leaf with mature sori on it and scrape the sori onto a folded piece of paper using a needle. If they are mature the sporangia should break open and release the spores onto the paper.

To propagate them I use small plastic containers with lids. The soil can be partially sterilized with boiling water. I pour the water over the soil and then tilt the container to get rid of the excess. Sprinkle the spores lightly over the soil once it has cooled. Cover and wait several weeks for the gametophytes to appear, which usually look like small heart-shaped prothalli. Spray the gametophytes occasionally with water to form a surface film which is necessary for fertilization. Then, after a few weeks or months, you should start to see the little sporophytes coming up. When they are several inches high you can gradually acclimatize them to dryer air and pot them up.

I agree with using containers like lycopus said.

I set my fronds on white paper and let them dry a day or so. spores will be released so long as the frond is ripe when picked. The paper will have both chaff and spores on it. The tiny brown specks are the chaff. The spores are almost impossible to see when spread out.
Tilt the paper and gently tap it until the chaff gets knocked off the paper. Don't worry about knocking the spores off, they stick to the paper fairly well. Don't put the chaff on the soil or you grow fungus instead of ferns.
After the paper is cleaned of the garbage. Hold the paper over the soil and start tapping the paper a bit harder. The incredibly fine dust (spores) should be seen working their way down the paper. Don't try to get them all on the soil, otherwise they'll be over crowded. (it ends up looking like moss and fronds never appear)

As for the soil, I put it in a glass or plastic container with a lid, lightly moisten it, then zap it in the microwave to sterilize it. after it is cool, I add a little extra water if necessary (only lightly moist) then add the spores.

good luck. remember have fun and be patient.