Examine your Sudoku grid carefully. The most important rule to keep in mind is that no number can be placed inside of the same row, column or region where it is already represented once. Try to find any numbers that appear several times throughout the puzzle. Because they have already been placed, there are very few options for drawing in your own.
Look at the available boxes once you have found a number that appears multiple times. As soon as you find a number that is already represented in every other region, row, and column, use your pencil to write that number into the appropriate box. Continue this process with all numbers that appear multiple times.
Use your pencil to draw very small numbers in the boxes where you think they may be solutions, but other solutions are also possible. Once you have several rows and columns set up in this way, you can simply look at them and mentally determine which combinations satisfy the rules of Sudoku.