Well, I used to start by chopping dry sphagnum in a blender until it is really fine. I have now switched to using peat (powdered form). The results with the peat are far superior in terms of health of the plants. Place this about 1 cm thick in a sealable plastic box. (Best to mist layers as you put it in or the bottom will stay dry with air pockets) you want it moistened but not so soggy that there's standing water. Some people use big plastic trays like you carry potted plants inside of, but I think they are mostly greenhouse growers that have very high humidity all the time. Then, just try to spread the spores evenly across the top surface (not too thickly or you'll never be able to transplant them individually!) and cover them. Leave in medium bright light but not direct sunlight, misting whenever they need it (depends on your cover).
After 1-3 months it will appear to have a fine green 'mist' on the surface. As time passes you'll see the first growths as transparent, filmy, circular
prothallium/gametophytes. (Like the first photo) These are still not fertilized 'beings' yet...the sperm need to 'swim' between the individual plants so you can't forget to keep misting.
After they are fertilized, they start to grow the first 'true' leaves (like the second photo of the P. Ridlyii) You can see them as little 'flags". Anytime after that you can start to transplant them to a new container so that they have room enough between plants to grow without crowding each other out. Again, I use boxes with peat moss, and a tweezers and/or a needle to move them. It's a little hard without a magnifying glass but they are pretty resilient, so just try to get them right-side-up! You can just set them on the surface, no need to "plant" them. And lightly mist them again so they settle onto the surface.
They are pretty slow growing for the first year to year and a half, but really start going after that. High humidity really helps and drying out at anytime while they are young is instant death!
Before you know it you will be looking to buy shelving units to store all your boxes as it is so easy you won't be able to pass a new species without collecting spores! By the way, this method holds true for almost any fern species. You just have to be there at the right time to collect the spores as they are ready to drop. Scratching off spores before they are ready to drop on their own is a waste of time.
I definitely recommend trying this and wish I had started doing it when I was younger...I'd have millions of them by now...well...I do anyway! But they would be much bigger! You will feel great being able to give them away to people or just start putting them in trees everywhere you think they will survive...help put the 'jungle-rapist' out of business! Better yet - teach them how to grow 'em from spores! There are a lot of websites that discuss growing Platyceriums from spores as well as numerous forums with helpful people where this is discussed (just like we discuss CP growing here). As mentioned above, Roy Vail's book is the best I have read on the subject.
Try It! Good luck growing!
And post your results!