For example, a par might be worth 1 point, a birdie 2. If you par the first hole and birdie the second, you've accrued 3 points.
As a format for club tournaments, Stableford is popular in the U.K., Europe and South Africa, among other locations; it is much less common in the United States. On the major pro tours, as of 2013, only the PGA Tour's Reno-Tahoe Open uses Modified Stableford scoring. (The U.S. PGA Tour and the European Tour used to have other Modified Stableford tournaments - The International and the ANZ Championship, respectively - but both those events are now defunct.)
The rulebook also sets forth points totals for a Stableford competition (Stableford tournaments that award points on a different scale than this are known as Modified Stableford):
More than one over fixed score or no score returned - 0 points
One over fixed score - 1 point
Fixed score - 2 points
One under fixed score - 3 points
Two under fixed score - 4 points
Three under fixed score - 5 points
Four under fixed score - 6 points
The "fixed score" in question is set by the tournament committee. If the fixed score is set as bogey, then a triple bogey is worth 0 points, a double bogey 1 point, a bogey 2 points, a par 3 points, and so on (the committee might also set the fixed score as a numerical value - say, 6 strokes - as opposed to a relative value).
The rules differences for Stableford as compared to normal stroke play have to do with the penalties applied for breaking rules. In some instances (for example, exceeding the 14-club maximum), points are deducted from the competitor, as opposed to a stroke penalty. There are also a number of violations that result in disqualification. The rundown of rules differences in Stableford can be found in the notes to Rule 32-1b and in Rule 32-2.
Modified Stableford on Tour
The Reno-Tahoe Open the PGA Tour (and The International and ANZ Championship before it) uses a Modified Stableford format (so-called because its points are awarded on a different scale from that described in the rulebook).
The pro tournaments use or used the same points scale:
Double bogey or worse - minus-3 points
Bogey - minus-1 point
Par - 0 points
Birdie - 2 points
Eagle - 5 points
Double eagle - 8 points
The difference between a rulebook Stableford and a Modified Stableford is usually reflected in the quality of the players. A traditional Stableford is appropriate for "normal" golfers (e.g., you and me), most of whom aren't going to be racking up birdies left and right. Therefore, the traditional Stableford's points system doesn't penalize players with negative points.
The pros, however, are in a different league. And the Modified Stableford scoring used in tour events harshly penalizes a disaster hole, but offers even greater rewards for very good holes.
Next Page: Strategy and Handicaps in Stableford