I've found that the kind of cheese that you use really matters a lot. I think I had the best luck with the Arrezio brand from Hallsmith Sysco. We've tried them in frying pans and on silpats. Do a search on the web for the word "frico" and see what you find.
Finely grate your parmesan (be sure not to use the rind, this will be tough)
Lay a thin (lacey)layer of the cheese on a sheet pan.
Make sure before you cook the cheese that you have everything you need to make your tuiles as soon as you pull the cheese.
(another words, your molds)
Bake the cheese until it starts to bubble and turn golden brown, at this time pull it from the oven, using an off-set spatula, gently release the cheese to a cutting board, cut your rounds or squares and put them on the mold and gently push them down to form your tuiles.
Let them cool and harden, and keep in a cool, DRY place.
Hope this helps and good luck
I make these all the time! Lidia Bastianich uses Montasio for this, but I use parmesan. There is a recipe in "Lidia's Italian Table". If you can't find it, please send me a private message and I'll type it up for you.
I have tried using parchment on baking sheets, Silpats on baking sheets, and a non-stick skillet. I like the skillet best of all. True, you can't make as many at a time, but I think the product is better. I suppose the cheese's moisture and fat content makes a difference, but a little experimentation should give you what you're looking for.
CC is right about the storage, but they usually don't last that long at my house! I make them about 2" for cocktails or larger if I'm making a little bowl for greens. I have also made them larger and cut them in wedges for variety.