There are a number of different strategies to solve a Sudoku. In this article I will present some of the simpler variety.
The simplest case is when only one field is left empty in a row, column or block. In such a case, you only have to look which number is still missing in this row/column/block and enter it into the free field. The following image gives an example of thiy type:
As we can see, in the eighth and penultimate row, eight of nine fields are already occupied. The only missing digit is the 2. So we enter it in the free field.
Of course, it's not always as simple as the example above. If more than one field is empty in a row/column/block, you have to try to find out if there is only one possible candidate in a field by scanning the other fields. In the following Sudoku puzzle, we look at the block on the bottom right.
The numbers 2, 5, and 6 are still missing in this block, so we look at columns 7, 8, and 9 because they are adjacent to this block and directly affect the missing cells. In the last column, the 5 and the 6 are already present. Therefore, only the 2 is possible in cell C. For A and B, the 5 and 6 remain. But in column 8 there is already the 5, so for cell B only the 6 remains. Thus, the 5 is the only remaining candidate for cell A.
In the same example, we can now look at the eighth column. There, only two digits are missing: 6 and 7. However, the 6 is already present in the lower left block, which is why we can enter the 7 in the third cell of the eighth column. For the last remaining cell, only the 6 remains.
Afterwards, you can proceed exactly the same way and solve the Sudoku this way.
In the following example there is only one possibility in the cell marked by the question mark.
In the same column, the 1, 2, 4, 5, 8 and 9 are already there and cannot occur again. In the same block there is also already the 3 and in the same line the 7. So only the 6 is missing, which we can enter for the question mark.
For more advanced Sudoku strategies you can check the great site sudokuwiki.org.