Keeping score can be a fun way to watch a ballgame. While it requires concentration, it's a great way to keep focused on the game. Longtime scorekeepers will often comment about how much they've missed in the game when not score-keeping.
There is a certain amount of information that should be recorded for each game. On a basic level and in support of the umpire, the scorekeeper needs to know: a) the count on the batter, b) the number of outs in the current half-inning, c) the current inning, and d) how many runs have been scored in this half-inning and in the game. There are additional division specific pitching and catching requirements to be met.
The league is asking each team to identify someone willing to be a scorekeeper. The league also recognizes that not everyone knows how to keep score. This page has been written to help guide the beginning scorekeeper and provide further resources. There are a great variety of scorecards and you will find no two people keep score exactly the same way.
Here is a beginner's guide to traditional score-keeping
Many other guides and methods can be found on the web.
has a score-keeping tutorial
and also a download
area for scorecards of various styles. If the link is down, the tutorial is here
has a good page and an excellent tutorial
on scorekeeping. Should the link be down, the complete tutorial is here
and the scorecard here
As you become more proficient in score-keeping, you will find judgment, interpretation, and even the application of playing rules becomes important. ASA offers very little for the official scorer but what it does offer will be found in Rule 11
of the Official Rules of Softball. Scorekeeping rules are defined by Rule 14. A standalone version of Rule 14 is here
may also be of interest. Lastly, there is softball's stick and ball cousin, baseball. Rule 10
contains the scoring guidelines for baseball.