Installing architectural foam?
 

How is this stuff attached to a surface with building paper and wire--mortar, Liquid Nails, or what?

Yup
 

The companies sell the glue you need. Certain glue for certain products. Stick it to it and caulk, don't penetrate the stucco, bad idea.

Here is a great idea for . For purchase best architectural foam visit Foam Supplies | Moulding | Stuco | Architectural Foam, building materials, EPS, Expanded.

Best Regards,