Sudoku Islands are based on a regular 9x9 grid with four additional shaded areas dropped on top. Each of these shaded areas will have each digit, 1-9, appear in them exactly once.
The most important thing to do when solving an Island Sudoku is to look at where each island overlaps a 3x3 box. Let’s say that seven of the shaded spaces in the island overlap a particular box. That means there are two spaces inside the box that are not in the island and, similarly, two spaces in the island that are not in the box. Since digits can’t repeat within a box or an island, the two digits that go in the box and the two that go in the island spaces outside the box must be the same. Although this won’t tell you where the digits go, it does reduce the possibilities.
Another useful trick is to look at Island spaces that you haven’t yet filled in. Let’s say you have two remaining spaces in an Island. One of them is in the same box as 3,5; the same column as 4,5; and the same row as a 7. This means that the remaining space must either be 3, 4, 5 or 7. You’ve probably solved regular Sudoku puzzles using similar logic, but it’s easy to miss with an Island puzzle.