Purchase a wine fridge that vents from the front for installation beneath your counter to avoid creating a fire hazard. Look for fridges that specify under-counter placement, as these will have the proper safeguards built in.
Measure the space available within your island with a tape measure, covering the interior height, width and depth of the island cabinet, and look for fridges that fit within the measurements.
Remove the door to the island cabinets using a Phillips-head screwdriver to remove the cabinet hinges holding the doors in place.
Install an electrical outlet beneath the island countertop if none is available. Check the fridge instructions for the necessary voltage, either 110-volt or 220-volt, and install the outlet necessary.
Run the wire for your outlet to the nearest electrical box in your kitchen by drilling holes through the kitchen flooring and running the wire beneath. Have an electrician perform the actual connections for you to ensure that the connection complies with local building codes, or you may create a fire hazard or leave yourself open to fines.
Place the wine fridge into the island. Plug the fridge into the outlet and then adjust the legs of the unit to raise it so that the top presses against the interior base of the countertop.
Push the unit far enough within the island so that the face of the fridge sits flush with the front of the cabinet frame.
Cut finishing trim to fit around the edges of the unit and fill the remaining space between the edge of the fridge and the cabinet edges. Use a wood that matches your cabinet so that it blends into the wood of the island.
Measure the partial spaces and then cut the trim with a circular saw to fit. Glue the trim to the edges of the cabinet with wood glue, and line the edges of the trim against the fridge with a rubber trim so that it fits snugly against the fridge edge.
Cut the rubber trim with a utility knife to fit along the wood trim edges.