You have TWO switches: 1 replaces your present in-wall WIRED switch, the 2nd switch is WIRE-LESS; it gets glued or screwed onto a convenient place on a wall.
The WIRE_LESS will NOT have a place to attach ANY wires, it operates off of a battery (9-volt).
The WIRED, in-wall replacement switch 'should' have a place to attach that bare copper GROUND wire, a green screw is the common method. BUT: many light switches don't!!. Unless the in-wall switch is outdoors or in a moist location (like within 6 feet of a sink, like your kitchen, bathroom, laundry sink or other water source), some switches will only have a black/hot/negative wire and a white/neutral wire. If you feel comfortable doing it, go to an electric-goods/electrical supply store where there is a knowledgeable person to help you (not usually found in those big-box stores!) and explain what you have; there is a type of metal clip that you can crimp onto the end of your ground wire and then crimp or otherwise attach to the metal tab/s of your replacement switch. Another thing: some of the new switches have a small slot, usually on the bottom of the metal tab of the switch housing that will accommodate the ground wire: slide the tip of the wire in that slot and then squeeze/crimp it with pliers.
If you're not comfortable doing electrical stuff, hire a licensed electrician.
And no matter what, TURN OFF the circuit breaker to the switch BEFORE you remove the old switch. That is ESPECIALLY important not only to prevent a shock, but ALSO if the new switch has a dimmer/rheostat function: ALL dimmer/rheostat switches have directions that state "Do NOT wire this switch HOT, always turn power off." That's a good thing to remember.
The following info is what I cut-and-pasted from the weblink you provided:
From the Manufacturer:
The BL-6133-WH Wireless Add on Switch provides the ability to add light switch control to any wired light without new wiring. Simply replace the existing wall switch that controls the light and mount the wireless wall switch in a new location. The wireless wall switch operates the wired wall switch within 100 feet to turn lights ON and OFF. The wireless wall switch requires a 9 volt battery, not included. Each wired wall switch controls 500 Watts incandescent lighting and fits inside standard wiring boxes.
Control a light from 2 switches without new wiring. - Features: Remote Control/Switch-easy install mounts anywhere, without wires. Powered by a 9 volt alkaline battery (not included). Battery typically lasts 1 year. - Receiver switch-easily replaces your existing wall switch. - Up to 100 Foot Transmission Range- Signal passes through doors, walls and floor. - Different Channels Available-compatible with other Heath/Zenith switches (same channel code). - 500 Watts Maximum- Control up to 500 watts of incandescent lighting. - Operates like a 3-way switch. - Trilingual Manual-Manual includes English, French and Spanish instructions. - Ideal locations include: Long hallways; large rooms with two entryways; top and bottom of stairs; detached garages. Anywhere you need two switches to control the same light.
handyman for many decades; I'm still alive because I follow directions/instructions...