The best way to attach mesh fencing to wood posts and rails is with galvanized U-staples. I suggest using staples no smaller than 3/4 inch for this purpose.
Red top brand and Bekaert dealer of wire fence, woven wire, hi-tensile wire, V-mesh, 2X4 no climb
Cheap Fence Ideas | Security Fencing, School Fencing & Pipe and Mesh Fencing
How to Build a Mesh Fence/detailed tutorial
Galvanized steel mesh fence with cedar frame - Loyal Heights, Ecoyards.
Ranch And Farm Fence Gallery | Farm Fences and Rail Fences, Installation, Design & Repair: VA Fence ...
Perfect example of what I want for my chicken wire/wire mesh fencing. A more long term "temporary fix" for my escape artist dogs.
Living Iron: Hog Wire Fencing with Patina, landscape design, fencing. Will it keep out deer?
Secure Mesh Fencing
Split Rail Fence With Mesh (I'd use wire. Still attractive but a great puppy barrier!)