Ensure the sides (where the couplers are) and the seat ends are all pushed together, and cut the rest of the wire leaving a 2" (50mm) overhang at every point.
Then, with a hammer, bend the overhangs over against the wood and fasten each bend with two galvanized staples.
If you prefer a more polished look (fastening-wise), another option is to make a thread on the ends of the wire, and then secure each end with a washer and dome nut.
This would mean leaving approximately a ⅜" (10mm) overhang on the wire at each point rather than the 2" (50mm) overhang and making a thread on the ends of the wire.
A thread can be easily made with a tool called a 'die'.
Finally, a bit of sanding.
Get rid of all the sharp edges and that's about it.