To attach a wall box: Buy a rework electric box (blue plastic rectangular box with tabs top and bottom that grip the wall from behind and tighten with screws). Draw an outline of the box on the wall and carefully cut out the rectangular hole with a key-hole saw. Route the wire into the box, then insert the box in teh hole and tighen the tabs into place. Attach the cover.
Easy way: buy a pair of plastic wall anchors. Mark the hole locations top and bottom of the plate and drill 1/4 inch holes in the drywall, insert anchors, attach cable to plate and attach plate to anchors.
If this is not clear, post back.