The fundamental rule of sudoku is that a number can only appear once in any row, column or box.

Consider this typical sudoku puzzle:

.4...8..9...297.....3.......8...4.7...6...9...3.9...1.......6..8..35...75..1.9.3.
In the starting grid below focus on cell r7c6:

Before starting, the cell r7c6 has the digits 1-9 as possibilities. If this cell
were to see a 1 in either its row, column or box, then the 1 could be eliminated. As it turns out, it can see the 1 at r9c4, therefore
the 1 can go. There is no 2 that r7c6 can see, so this remains a possibility. There is 3 at r8c4, 4 at r4c6 and so on so that the
only number that can legally go into r7c6 is a 2. Having solved r7c6, focus on r8c6. Now one can see that only a 6 can be placed
there. Focusing on cells that can see the most given or solved cells, another 8 cells can be solved as shown below:

The remaining unsolved cells can be populated with numbers that comply with the fundamental rule to achieve the above grid.