Laminate flooring is installed by snapping together 3-foot sections that have a tongue-and-groove locking mechanism to hold them together. When you lay a laminate floor around an obstruction like a kitchen island, it is easier to start the installation around that obstruction and work away from it. This will minimize the amount of cutting you have to do and the number to tight gaps into which you have to fit the flooring.
Level the floor and seal the gaps with floor-leveling compound and sand the compound flat with a belt sander when it dries. Do not leave any protrusions because you will feel these when you walk on the floor. Vacuum the floor when you are finished.
Spread a vapor barrier over the floor and staple it down. You can buy a foam barrier from a laminate dealer that will make the floor more comfortable to walk on as it protects against moisture.
Open the boxes of flooring and let the boards acclimatize to the room for three to five days before you install them.
Begin the installation by laying a course of flooring along one of the sides of the island and extending it to the wall or cabinet on either side of the room. Then work away from the cabinet, installing the next course with the ends staggered at least 6 inches from the ends of the first course. Click the boards together by lifting on one side or end as you push the boards together or use a tapping block and a hammer to tap the boards together. Using a circular saw, rip the boards next to the wall to fit, and use a pry bar to pry them to the adjoining boards.
Lay the flooring around the island by working toward the opposite side of the room and cutting the first board in each course to maintain the stagger pattern you have established in the rest of the floor. When you get to the other side of the island, carefully measure the distance from the edge of the floor to the edge of the island, and notch boards to fit. Make the straight cuts with a circular saw and cut out the corners with a jigsaw. Tap the boards into place with a tapping block.
Lay the rest of the floor, maintaining the same stagger interval, until you get to the opposite side of the floor. Cut the last course to fit and pry it into position with a pry bar.
Install baseboards around the perimeter of the floor and around the island by fastening it to the walls or cabinets with finish nails.