How to play Killer Sudoku
The rules of Killer Sudoku are based on those of Sudoku, since you must place each of the numbers 1 to 9 (or 1 to whatever the width of the puzzle is) into each of the rows, columns and bold-lined boxes. Additionally, however, you must also place the numbers so that each dashed-line 'cage' adds up to the total given at the top-left in smaller digits. For example, the first two squares on the first row of this puzzle must add up to 10. You also cannot repeat a number within a cage, so this means for example that the solution to '4' must be 1 and 3, not 2 and 2 (although 2 and 2 would be disallowed by the standard rules of Sudoku in any case).
By marking some of the 'only fit' numbers in as pencilmarks, and observing that there is only one cage into which a '2' can fit in the centre column, we can start to solve the puzzle:
No numbers have yet been placed and there is a long way still to go, but by using logic alone every killer sudoku puzzle can be solved! There is never any need to guess.
Continue to solve the puzzle using both regular Sudoku logic and a range of possible deductions unique to Killer Sudoku, and you will eventually reach the final result. When the puzzle is fully-solved you will have 1 to 9 in each row, column and 3-by-3 shape, and each cage will add up to the total at the top-left:
Once you get really good at Killer Sudoku, you might even find you can solve some of them faster than standard Sudoku!