The principles for FIS, BASS and BARTS are roughly the same, but there are a number of differences in detail - partly historical, partly to be less complicated than FIS.

The basic calculations are shown below for each of the above; there is also a link to each of the respective rules for further reading.

FIS RULES

FIS Points
The Average of the Best Two Results
The average of a competitor's best two results in each discipline during the
Validity period will be used for the evaluation of the FIS points.
The Double Penalties
Discipline Double Penalty
44%
Downhill min. 8 - max. 52 points
Slalom min. 8 - max. 28 points
Giant Slalom, Super G min. 8 - max. 40 points

Only one Result
For a competitor who has obtained only one result in Downhill, Slalom, Giant
Slalom and Super G during the validity period, a double penalty will be added
to his result.

FIS rules: http://www.fis-ski.com/data/document/fispts06.pdf See Section 4

BASS RULES
Calculation of Race Results for British & MG (non-FIS) and Club races

Race Points. These are calculated by the formula:
P =( (Tx - To)/To) x F

where
P = Race Points
Tx = Racer's Time in seconds
To = Winner's Time in seconds
F = 'F' factor, announced annually for each discipline.

Race Penalty Point.
The Race Penalty Point (RPP) is calculated as follows:
RPP = (A + B - C)/10

where
A = Seed Point total of those 5 racers who started the race who have the lowest BASS
seed points
B = Seed Point total of those 5 racers in the first 10 BASS registered finishers who have
the lowest BASS seed points
C = Total of Race Points of the corresponding 5 finishers

BASS rules: http://www.britski.org/bcr2004.pdf See Part 5 Sections 5, 6 & 10

BARTS RULES
1721.1 For each competitor:
Race Point = (Competitor's Time 1) * F

Winner's Time
The value of F shall be as published by FIS for the appropriate race discipline.
1721.2 A "Race Penalty Point" (RPP) shall be determined using the following formula:
Race Penalty Point = (A + B C)/10

where
A = the sum of the Snowsport England seed points of the 5 best seeded competitors in the first 10 finishers
and B = the sum of the Snowsport England seed points of the 5 best seeded starters in the race
and C = the sum of the Race Points of the 5 best seeded competitors in the first 10 finishers.

BARTS rules: http://rotp.snowsportengland.org.uk/rules/SSERM66.pdf See Section 1700

The information shown above was given to us curtsey of Peter Heath of www.britski.org, Thank you peter!