How do you attach these to walls?

I suppose you could use most anything, I used an air brad nailer, the kind you install moldings with, into furring strips. That makes for an almost invisible fastener, of course if you don't happen to have a compressor and nail gun (but brad nailers are cheap), you could just use small brad nails. Because it is a white finish, you can just touch up any fastener heads with a spot of paint. The tops and bottoms would likely be behind some sort of molding anyway. The material is sturdy enough so small fasteners work well and you won't need a lot of them. Glue should work fine, but I always have a gnawing fear that I might want to remove a panel for whatever reason, once glued that's difficult.

With this kind of product it is up to you and what makes you feel better using to complete the task.