It is literally the reverse of how it was installed. Check underneath for any fasteners. Any caulk should be cut with a knife.
Good advice from Cynthia, she makes it sound so simple and it is no matter what your island countertop is made of. If it is very heavy-such as granite, take precautions so as to not hurt your self or break it.
Laminate countertops on islands are screwed in from the bottom.
Remove items from the cabinets, and crawl into the island on your back, so that you are looking up at the underside of the countertop.
You should be able to see screws or bolts.
Then, as Cynthia said, simply unscrew, then lift the countertop off.
Laminate countertops will have two sides that have a finished edge, and two sides with a flat edge. A thin layer of laminate stripping is 'heat applied' to cover the two unfinished flat edges.
Solid material countertops such as Corian, quartz, or granite have all four sides that are finished. They can also be molded into curved shapes such as circles.
One of the reasons why solid countertop materials are higher priced than laminate is due to increased durability in the edges, as they are all seamless.
Common choices in countertop edge finishes , called profiles, are below.