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Two types of scoring are seen in pairs tournaments - Matchpoints and IMPs (Butler).

Most seasoned tournament players know the scoring rules inside out, and even change
the way they play depending on the scoring method. However, newcomers to
tournament bridge are in the dark - they are told that in Butler, they should ensure the
contract; and in Matchpoints, go for notrumps and overtricks! This is basically good
advice - though not fully accurate.  

Here, I want to explain how the scoring is done.

1. Matchpoints:

In matchpoints, on any board, you get -

one point from all the pairs who scored less than you.
half a point from all the pairs who have the same score.

The actual difference in scores is immaterial; what matters is whose score is higher.

e.g. say board 10 is played on 5 tables:

NS   EW   NS Score  NS MPs   EW MPs   
 1      6         620         1.5         2.5
 2      7        -100         0             4
 3      8         630         3             1
 4      9         620         1.5          2.5
 5     10       1100         4             0

NS no.5 get 4 Matchpoints (a 'top') for their +1100. Note that they would still get a top
even if they got +800 - for that matter even if they got +640!

NS no.3 get 3 MPs out of 4 because they played in 3NT instead of 4H(or 4S) and made 10
tricks. Had they made 9 tricks for +600, they would get only 1 Matchpoint.

The TOP on a board depends on the number of tables where that board is played. If a
board is played on 13 tables, the top is 12. In Shubhmangal, where we sometimes
duplicate the boards and play them in two sections, each board is generally played on
26 tables and so the top is 25 matchpoints.

2. IMPs or Butler scoring:
 
In Butler scoring, we take the average of all the scores on a board (the top and bottom
20% scores are first removed to avoid the wild scores). This average is called the
'Datum'.

The difference between each score and the datum is then computed. This difference is
converted to IMPs (International Match Points) using the standard IMP scale.

Let us take the same scoresheet:

NS EW NS Score
 1    6     620
 2    7     -100
 3    8     630
 4    9     620
 5    10   1100

The top and bottom scores are removed - this leaves three scores - 620, 630, 620.
Average is calculated and rounded off to 620. So, the datum on this board is +620. The
plus sign indicates that the datum is in the NS direction.

Datum : +620
NS EW   NS Score   Diff.    NS IMPs  EW IMPs
 1    6         620          0           0            0
 2    7        -100       -720       -12         +12
 3    8         630          10         0            0
 4    9         620          0           0            0
 5    10      1100      +480      +10         -10

Here, NS no.5 got +10 IMPs. If they had scored +800, they would get +5 IMPs.

Also, a difference of 10 is converted to 0 IMPs.. so there is no incentive to play in No Trumps
instead of suit contracts, as is fashionable in Matchpoints.

Overtricks are less important too - in matchpoints an overtrick may get you a Top, but in
Butler all you will get is 1 IMP.

 http://www.rpbridge.net/7d63.htm