Stone Counting
There are two concepts that may both be called "Stone Counting". The original meaning referred to a form of scoring.
Traditional Chinese Scoring
For information about the ancient scoring method based on the counts of alive stones, which is sometimes also called "Stone Counting", see Stone Scoring.
Stone Counting Method
Games played under rules with Area Scoring can be counted using an easy method based on filling in. The method is well suited for beginners when playing on smaller boards. This method results in the modern Area score, which doesn't include the 'tax'.
The library has complete instructions on the Stone Counting Method and there is an example.