In each Sudoku puzzle you have a 9x9 grid, divided into nine 3x3 square regions (you can just look above to get an impression). So each row, column or region contains nine cells.
You start a Sudoku puzzle with some cells already filled in with numbers. You can't change these numbers. The more cells are pre-filled the easier the puzzle. Now you just need to fill the remaining cells with numbers from 1 to 9, obeying the only rule:
Each row, column or region must not contain repetitive numbers. So each number from 1 to 9 occurs only one time in each row, column and region. Sounds like a tricky task? Just start scanning the board and you'll find all clues you need, one by one, and get the puzzle solved.
Start a Sudoku puzzle on an Easy level to learn all the techniques quickly. You will certainly see a square where just one or two numbers are missing. For example, if a 3x3 square lacks just the numbers 3 and 7, we have only two options on how to place these two remaining numbers - 3 in a first cell and 7 in a second one or vice versa. Which one is correct? Just place 3 and look across the whole row, then the column: is there a duplicate? Try the same with 7 and you'll get the correct option.
Now try to use the same technique but now with an almost filled-in row or column - find the one where only one number missing (then the answer is obvious) or two ones missing - try both options and figure out the right one.
Now you will notice the more and more rows, columns and regions become almost complete and easy to deduce - the complete puzzle picture becomes clearer with each move.
The more advanced technique you can use for a harder puzzle called 'scanning': it exploits the fact that any given number from 1 to 9 can occur only nine times in a completed Sudoku puzzle. Choose a number that occurs most on the board already (so there's one or two instances left to place) - there are indicators below the board to help you find the best one. Let's say it's the 4. Now draw a horizontal and vertical line from every 4 on the board (you remember you can't place another 4 in a row or column) - it will quickly become clear there are almost no cells left where you can actually put it.
No matter what trick you use the most helpful thing for solving a Sudoku is 'penciling the candidates'. Just like in a paper Sudoku, you can make 'small pencil notes' in the cell of which numbers can go there. Just click the 'note' icon - now every number you put in a cell will be a small note alongside other candidates. Just click the icon again to switch to placing big 'final' decisions (you can erase any of these too in case you change your mind).
Of course 'Undo' and 'Redo' can be helpful too - the icons are just right of the board.
And be sure to open the Settings page (using the gear icon) and try various error highlighting modes - that's the indispensable tool for getting the hand in quickly finding the right candidates.