The Olympic Canoe / Kayak rules and scoring are derived from the standard international rules as set forth by the International Canoe Federation, or the ICF. The rules and scoring for Olympic Canoe / Kayak are actually very straightforward and self explanatory. The fastest boater wins. Of course there are more specific guidelines which you can read about here.
Canoe / Kayak Flatwater Rules and ScoringThe Canoe/Kayak Flatwater Competition is won by the person who reaches the finish line of an unobstructed course in the shortest amount of time possible. Paddlers must stay in their lanes for the duration of the race. There must be at least 3 canoes or kayaks in each event. If multiple heats are required, the total number of canoes or kayaks in each heat must not exceed 9. This event is only open to members of an ICF National Federation club or association. Gold, Silver, and Bronze medals are awarded in all Olympic Canoe / Kayak Flatwater events.
>Canoe / Kayak Slalom Rules and ScoringThe Slalom Racing Competition is won by the competitor who scores the shortest time while navigating the turbulent 300 meter course. There are a series of 20-25 gates situated throughout the whitewater rapids. The gates are labeled with either red and white stripes or green and white stripes. The green and white striped gates must be paddled through while going downstream while the red and white gates must be gone through while paddling upstream. The gates are suspended above the river and are placed in such a way that the paddler must utilize the various river features surrounding the gates to get through them. A two second penalty is assessed for touching each gate as it is gone through. A fifty second penalty is added to the paddler’s time for missing the gate altogether. Gold, Silver, and Bronze medals are awarded in all Olympic Canoe / Kayak Slalom Racing Events.
Read more at What is Olympic Canoe/Kayak?