Scan and Eliminate Numbers
This is one of the most basic solving methods, which can be used at the beginning (and can be repeated after finding one or more numbers with one of the other solving methods) of the puzzle. At the beginning the puzzle could look like our example :
Basically every cell contains the possible solutions 1 to 9. By using the given numbers you can eliminate many possible solutions.
Look for example at cell A1. The possible solutions for this cell are : 1,2,3,4,5,6,7,8,9.
In the first row (rows are horizontal and columns are vertical in case you are wondering) we see the given numbers 9,8,2,5 and 6. Because every number can only appear once in a row, we can eliminate the given numbers from the set of possible solutions.
This means that the following numbers will be left: 1,3,4,7
In the first column we have the given numbers 2,3,5 and 8. These numbers can also be eliminated from the set of possible numbers in cell A1. After elimination the following numbers are left 1,4,7.
The 3x3 box gives you the numbers 2,6,8 and 9. Because al these numbers are already eliminated from the possible solutions, nothing will change anymore in cell A1.
This gives the final result of possible solutions 1,4,7. These numbers will be noted in cell A1.
You have to repeat the above described procedure for every cell. If lucky you can eliminated all but one numbers in a cell, leaving you the solution for that cell.
After you have finished eliminating all candidates, the puzzle will look like the one as shown here.