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Stars is one of a number of puzzles that require you to identify isolated cells in a grid of irregular shapes. Another such puzzle is Suguru.
The eponymous stars have no particular relevance, they are an appealing icon to place on the isolated cells in each shape in the rather forbidding empty grid. The given constraints are all the reader requires to solve the puzzle. There are four levels of difficulty. Easy puzzles are 6x6, other levels of difficulty are 9x9. The example puzzle has a medium level of difficulty.
Each row, column and region must contain two stars. Star cells cannot touch, even diagonally.