I made a facial prosthetic out of air-dry clay, how would I attatch it?
That material is not likely to survive very long. Normally you would make the piece out of latex or silicone, because those materials are resilient. However, I can recommend that you use rubber cement. It is generally (unless you are allergic, which you can test by putting a small dab on your skin, if it itches or get red, wash it off immediately with warm soapy water). Assuming you are not allergic, now try to attach another sample as a test to your face. Figure out how much glue and how strong the clay is. Do this by applying the cement to the back of the clay and immediately attach it to your face.

If it works, then do it with the final piece. Good luck