Solving a sudoku puzzle is not as complicated as it looks. However, some people get caught up solving sudoku puzzles by guessing the missing numbers, then checking to see if the guess is right. The guessing strategy might work in the end, but getting there will be frustrating and quite a chore. The key to success is to systematically apply a specific solving strategy and an easy way to do it is to concentrate on one part of the grid at a time.
Write down all the numbers that are missing from the upper left box of nine squares above the square. Each 3 by 3 square can only hold the numbers 1 through 9, and each number can only appear once. Repeat the process going around the rest of the nine square boxes and writing down the missing numbers. Write the missing numbers from the middle square at the bottom of your sudoku puzzle.
Pick one of the missing numbers from the top left nine square box. Look across the top row to see if it contains the missing number. Each row will contain the numbers 1 through 9, and each row will only use each number once. If the row contains the number, the missing number cannot belong to that row. If the row doesn't contain the missing number, then the number could possibly go in that square. Look at the second and third rows to see if the missing number appears in the row.
Look down the first column to see if it contains your missing numbers. Each column will contain the numbers 1 through 9, and each column will use each number only once. If the column contains the number, then the missing number cannot belong to that column. If the column doesn't contain the missing number, and the row doesn't contain the missing number, then the missing number could possibly go in that square. Look at the second and third columns to see if the missing number can fit.
Pencil in the missing number in the upper left corner of any square which could contain the missing number. Move on to the rest of your list of missing numbers and repeat steps 2 and 3. If a square has only one possible number, then the missing number belongs in that box. Erase the numbers in the upper left corner of the square, and write the correct missing number in that square. If the box contains two or more possible numbers, you can't be certain of the correct number and more solving is necessary.
Repeat steps 2, 3, and 4 on the remaining eight boxes. When finished, look back at any rows, columns, or 3 by 3 box and erase any potential missing numbers from the top left of each square that have already been filled. Using process of elimination, work your way around the entire 9 by 9 grid until you have erased all potential missing numbers and filled in every square with a missing number that fits.