I made most of my islands from a lightweight plastic sheet that my workplace uses for signs at conventions. It's about 3/32" thick, made of two thin, vinyl-like outer sheets sandwiching a softer, porous inner layer. I have no idea what it's called or where to buy it. I just scrounge the discarded signs; one 2x3' sign board yields dozens of islands.
Each island starts as a square or rectangle, scribed with a knife and snapped off. I then cut the rough outline with a milling-machine bit in a bench drill press, and file it with a hand file to clean up the edges and put a bevel on them. Then I paint them with acrylic paints (from my miniature-wargaming hobby), and while the green paint in the middle is still wet, sprinkle on "grass" (ground foam from my model-railroading hobby). On the few islands with raised hills, those hills are small pieces of the same plastic, shaped entirely with hand tools — they're too small to safely hold to the milling bit. The houses on the home islands are from an old Monopoly game.
I tried to make each island a different shape. Not only does this make the game area more interesting-looking, but the more distinctive islands will acquire their own names. My game area includes Dogbone Island, Starfish Island, Round Island, and Porkchop Island. This makes for more lively dialog during the battle, and more descriptive battle reports afterward.
If you play with younger pirates, as I often do, it's fun for them to have their own islands. I make one in the shape of each pirate's initial. This can serve either as their own special home island, or as a special destination in a scenario. The latter can be hard to arrange if your group includes an Anthony, an Aimee, and an Abigail (as mine does), but if you're clever, you'll find a way.
The volcano is a chunk of pink insulating foam, hacked into shape with a sharp X-Acto knife, then had its surface scratched and gouged with the back of the knife tip. Then I painted it and glued it onto a plastic island with real sand (painted black) on it.
The large circular islands are made of old CD-ROM's with various landforms glued onto them. Humpback Island has four hills made of pink insulation foam, shaped with a file and painted as above. Sandbar Island is a plastic island glued onto a CD, which I then painted to look like water.
There's no limit to what you can do, once the idea hits. Dry Tortuga, which is mentioned in the battle reports, is a CD divided into four quarters: the shipyard (with a ladder-shaped slipway made of square toothpicks), the money changers (a Monopoly house with a dollar sign painted on the roof), the treasure field (dyed sawdust "grass" with a Pirate coin glued in the middle), and the tavern (another Monopoly house).