I would like to know the same thing.

The fencing probably is "stapled" to one piece of wood using heavy duty staple gun or hammer staples. Even if not, clearly its sandwiched between two pieces of what appears to be 2x2 boards which could be screwed together. It actually looks like pressure treated wood (exept for the pergula type thing), which would make sense because it will hold up in any weather.

For added stability cut off the flush sides of the wire to leave the vertical and horizontal ends exposed. Bolt cutter or grinder. Drill holes in the lumber for the wire end to push into 3/4-1". U can use wire fence staples as well but they are more prone too rust than the wire.

For added stability cut off the flush sides of the wire to leave the vertical and horizontal ends exposed. Bolt cutter or grinder. Drill holes in the lumber for the wire end to push into 3/4-1". U can use wire fence staples as well but they are more prone too rust than the wire.