Any tips on drying fresh cayenne chilies?

Solid recommendations about "air drying" the chills. One suggestion though, after you wash+dry them thoroughly, put a small slit along the body of the pepper so air can get inside and help the process along.

I have been in this situation before- I harvested 20 pounds of serrano chiles in one week from my garden once! The good news is that they dry beautifully and easily. I was living in California at the time so it was really dry and all i needed to do was spread them out on a flat surface and they dried on their own, but we also strung a lot of them on thread and hung them up. I think the key is not piling them, giving them room so that air can circulate. Once they are dry, still pliable but shriveled, i put them in jars and keep them in a dark cabinet. They smell like spicy dried berries. I'll check back if you have any other specific questions, but it is really an easy process- good luck.

Freeze them. Works just as well as drying and you don't have to worry about mold or rotting chiles.

If you really want to dry them, leave them, unplucked from the plant. Cut the whole plant or branch down. Gather all the plants/branches and tie together. Then hang the bouquet in a well ventilated room that is relatively cool and dry. Alternatively, you can pluck the chilis from the plant. Lay in a single layer on a tray or towel and leave out in the sun to dry. As long as they aren't overlapping and there's good air circulation, they will dry without rotting or molding.