To complete a Sudoku puzzle, you must fill each row, column, and each 3-by-3 group of squares with the numbers from 1 to 9, with each number appearing exactly one time in each row, column or 3-by-3 group. Here's a completed puzzle:
Each row, column, and 3-by-3 group of squares (indicated by the shading) contain the numbers 1 through 9, with each number appearing only one time in a row, column, or 3-by-3 set of squares. In the following puzzle, look at the 1's in red:
There are 1's in the first and third column. The 3-by-3 group in the lower left must have a 1 in it somewhere. The red 1's prevent any of the blue squares from having a 1 in them, because there would be two 1's in a single column. It must be one of the two yellow squares. But which one?
The blue 1 in the second last row is the clue you need. It cannot be in the lower yellow square, because there would be two 1's in the same row. The yellow square to the right of the 5 must be a 1. This is just one rule you can use to solve Sudoku puzzles. Discover the others for yourself!