Hi Mary,
Average lap racing is pretty commonly used for handicap racing in the UK (and, by Dermot's post, in Ireland too). My club uses it for all our dinghy and cat racing and it's also used by SNECCA (the Scotland and North of England Catamaran Class Association) for all their events.
The fleet starts as normal and sails round the course until they're told to stop - you don't know how many laps you're going to do when you start but you may well know roughly how long (timewise) the race will be. You have to set a course with identical laps - windward/leeward, triangles, trapezoids etc are fine but the old Olympic sausage/triangle isn't a good idea. Boats must go through the finish line at the end of each lap.
The RC records the time each boat passes through the finish line. At some point they decide the race has lasted long enough and put up flag S. Everyone who crosses the finishline after that is finishing the race. The result is then worked out on an average lap time - your elapsed time divided by the number of laps you do and the handicap is then applied. It may well be that everyone does the same number of laps but this very often isn't the case, particularly if there is a big spread of handicaps. And there is no need for the boat that is leading on the water to be the first boat that gets a finish. The RC can decide to stop the race at any point - they might do that as some very slow boats are approaching the line for example.
The system usually works well. By letting fast boats do more laps than slow boats you can compress the period that boats are finishing. So it is more likely that everyone is racing in similar conditions. And in a regatta it means the fast boats may not have as much hanging around between races.
George