Sudoku has several variants, but in the classic puzzles the rules for play are very straightforward. Each puzzle consists of a 9x9 grid - each cell of the grid must contain a single digit between 1 and 9. The puzzle is initially provided with some digits filled in, and the remaining cells must be solved. Harder puzzles have fewer initial filled digits and generally will take longer to solve than puzzles with more filled digits.
When placing digits, a few rules need to observed; every row, every column and every 3x3 subgrid must contain each digit (1 to 9) once and only once. Placing a digit thus rules out other digits from the same row, column and subgrid. Each puzzle should have only one correct solution that allows the grid to be filled entirely without violating the rules for uniqueness.
The solver must rely on logical deduction rather than guessing to reach the correct solution, and therein lies the appeal of Sudoku. A broad range of different solving strategies can be applied and some can be incredibly complex, but don’t worry - easy puzzles can be solved with a few simple beginner strategies. More advanced puzzles will require more advanced strategies.
One vital technique that can be applied at all levels of play is to use candidate numbers (also known as notes) - these are the potential possible numbers for a given cell. A cell with no filled numbers in the same row, column or subgrid could contain any of the 9 digits so the candidate numbers are 1,2,3,4,5,6,7,8 and 9. Any filled numbers in the same row, column or subgrid eliminate that number as a candidate from the remaining cells. If you see only one candidate number in a given cell, then that must be the correct number so the cell can be confidently filled. This in turn should then eliminate other candidates allowing further progress.
There are lots of different strategies for solving Sudoku puzzles and generally you will need to apply a number of different strategies repeatedly to solve a puzzle. Simpler puzzles will require just a few basic strategies whilst the most extreme puzzles will need repeated application of exotic approaches. As a rule of thumb, try the simplest strategies first - these are roughly shown in order below - and work up to the more complicated strategies only when needed as they take longer to figure out mentally. Usually this approach leads to the fastest solution for a given puzzle.