Players don’t really need to understand scoring. They do need to understand that scoring is a two stage process, first there is the hand score and then the match score.
Board Scores
Players usually just work out a board score by entering it into a Bridgemate (or similar) or looking up a table. But there are a few things to remember.
The first thing they need to remember is that you get a bonus for bidding and making a game. The second is that for the same number of tricks you get more points in No Trump than in a Major and more in a Major than a Minor. Third they need to know that there are big bonuses for bidding and making a slam.
Overall they need to remember that the bonuses above and the penalties for undertricks are increased if you are vulnerable.
Match Scores
Match scores (or event scores) are based on one of two systems. A club duplicate session is usually based on Matchpoint scoring while a Swiss Pairs or Teams event is usually based on International Match Points (IMPs) converted to Victory Points (VPs). That said an ordinary duplicate session can be IMPs scored while a Swiss Pairs can be matchpoint scored.
Matchpoint scoring
The pair’s score for each board is ranked against the scores of all other players on that board and maximum points are awarded to the highest ranked player. This means hat being in the best contract and making it isn’t all that counts, overtricks matter. If every NS pair in a nine table (Mitchell movement) duplicate pairs bids 4 spades and everyone makes it but only one pair makes an overtrick, that pairs scores 100% and all the others score 43.75%.
International Matchpoint scoring
In pairs, the difference between a pair’s score for a board and the average of the scores by all pairs sitting in the same direction on that board (the “datum”) is calculated and then converted to IMPs via a table. Typically Swiss Pairs events are actually Butler scored (even though it is not stated) in which case the top and bottom 10% of the scores on a board are excluded before the average is taken.
An alternative is Cross IMPs (or X-IMPs) scoring where the difference between a pair’s score on a board is subtracted from the score by each other pair sitting in the same direction, each of these is converted to IMPs and the score is the average of these. To put it mathematically, in the first we take the difference from the average in the latter we take the average of the differences.
For teams events the score at one table is subtracted from the score at the other table to get the difference that is converted to IMPs (practically, the score from the NS pair in the team is added to the EW score). So if both tables bid and make 4S by N the difference is zero. If only one bids to 4S but the other doesn’t and both tables N makes 10 tricks the difference is 350 which is converted to IMPs as positive for the team that bid the game and negative for the team that didn’t.
Making overtricks is much, much less important in IMPs scoring, bidding and making all the possible games is mu8ch more important.
To dampen the effect of very high board scores on totals, and to allow for different numbers of boards, the total IMPs for a match are converted to Victory Points (again using a table).
For more detail see the guide Understanding Bridge Scoring.