Let's have a look at a puzzle which has had all of the possible numbers counted out and written down:
The technique we've just been using takes advantage of the fact that a number can only occur once in a given row, column or 3x3 block. The next technique takes advantage of the fact that each number from 1..9 must occur once in each row, column, or 3x3 block. This means that if a number occurs only once in a particular row (or column, or 3x3 box), then that must be the correct number, even if there are other "possibles" written in the same square. Have a look at square [2, 3] in the puzzle below:
If we look at column 2 (highlighted in pale green) we can see that the number 4 occurs in only one square, [2, 3] (highlighted in dark green). This means that this square must contain 4, despite having more than one possibility written down. Fill the square in with 4, and don't forget to cross out any other 4s you find in the same row, column, or 3x3 box. In this case, square [1, 3], immediately to the left, has a 4 which can now be eliminated, as we know that any number can occur only once per row.
Next we'll be looking at quite a high powered technique, using pairs and triplets of numbers to eliminate possibilities elsewhere on the board, in Tutorial 4.