They are actually pretty easy. I have grown mine in a standard plastic, hanging basket--bit easier to keep it moister in the dry, interior Winters. A lot of people mount them though on wood or just suspend them. I use a loose soil (sphagnum moss, some wood or bark chips). You can hang them outside in the milder months. I hang mine under a Japanese maple where it can enjoy some dappled sun. They can take some direct sun but avoid hot, burning sun. I feed mine very lightly--a bit of fish emulsion once in a blue moon. I overwinter mine in the basement where it's humid (artificial light). Actually, they are among the easiest of the true ferns for overwintering in the house. Good luck!

My personal experience with them.

They get heavy and lopsided, so you'll want to mount them on something or find some way to weigh them down to keep them from flipping over. Mine's in a metal basket with a coconut coir liner and a bunch of sphagnum moss, which doesn't hold enough water to rot it or anything.

They don't seem to care about humidity that much. Having some humidity is probably a good thing, but it's not like some ferns that start falling apart if the relative humidity in your home dips below fifty.

Light's also not a huge issue. They won't die in lower light, though they won't grow. They don't really grow regularly throughout the year, but sort of in spurts.

Shield fronds normally turn brown. Fertile fronds only last about three years before dropping off.

Water I've never honestly figured out. I initially heard they were rot prone and that you shouldn't water them until they wilt. I used to do this and ended up killing one. This was when I was new to plants, though. The typical water-when-dry method seems to be the best bet.

What's odd though is that they're sort of succulent, especially when they get older because the mass of shield fronds acts like a sponge and stores water (and the fertile fronds seem succulent too, but I'm not sure). So, the one I have that I didn't accidentally kill... well, it's outside, it hasn't wilted or behaved strangely at ALL this summer, and I haven't been watering it that much. So I'm going to guess that smaller plants need more water and larger plants don't.

A platycerium will do fine outdoors for most of the year in Ohio. I live in Chicago, and during the winter my staghorn lives in the shower so it can get bright diffused light, free drainage, and plenty of humidity. The growth rate slows, but not by much. Just cut down on the watering when you bring it inside and you should be fine!

Thanks everyone for all the advice.