Sudoku Techniques : Pencilmarks
Most paper-and-pencil Sudoku players tend to come up with their own systems to help them complete the grids. Very few players complete puzzles only by writing in the final numbers!
Have a look in this incomplete puzzle:
The most common way to annotate grids is by writing in tiny numbers - usually referred to as "pencilmarks" - which really mean "this number is still possible for this cell."
You may be able to narrow down a cell to only contain "5 and 8" but not know which one. If you write a tiny 58 in the cell, then later on you may make another placement which allows you to cross off one of your pencilmarks. So, if you crossed out the 5, you know that the cell can now only contain an 8, so you can erase both pencilmarks and write in the large 8.
This example is computer generated, and shows all of the possible pencilmarks that could be added. You don't need to add in all of the pencilmarks - good players find it slows them down too much for the easiest puzzles, but need to use them for trickier puzzles.
Writing in all of the pencilmarks for every cell is quite a laborious task, but a computer program can do this automatically, updating the pencilmarks for cells whenever you add in a new value. Using pencilmarks makes it very easy to spot Single Candidates! (See the lone 3 in the top right 3x3 block)