Drill a 1/2-inch-diameter hole through the exterior wall of your house in an inconspicuous location. that is lower than the kitchen floor and that enters into the basement or crawl space. You may need to buy or rent an extra-long drill bit to accomplish this.
Measure the distance from the propane tank or natural gas hookup to the location of your kitchen island along the route that your gas line will take. Add 2 feet to this measurement as a margin of error and cut a piece of 3/8-inch-diameter flexible copper tubing to this length.
Connect the tubing to the propane tank or natural gas hookup. Depending on the nature of the tank or the hookup, this can be done in a number of ways. Usually it involves putting a threaded fitting onto the tubing, flaring the end of the tubing and screwing the flared end onto the nipple of the propane tank.
Feed the tubing from the tank through the hole in the exterior wall into the basement area. Run the tubing to a point directly underneath the kitchen island, supporting the tubing every 2 feet with a cleat nailed into the side of a joist.
Drill a hole through the floor into the kitchen island. Feed the copper tubing up into the kitchen island.
Attach the tubing to the cooktop using the same steps that you used to attach the other end to the propane tank.
Check both connections for leaks by spreading soapy water onto the connection, turning on the gas and watching for bubbles. If you see any, turn off the gas immediately and re-connect the fitting.