

Four race distances are used in international competition. Not all distances are used in all competitions. For example, the Olympics and the World Juniors don't race the 3000m.
With the exception of the Olympics, competitions takes 3 days. The 1500m is on day 1, 500m on day 2, 1000m and the 3000m on day 3. Relays are race each day with the relay final occurring on day 3.
500 meters: The 4½ laps of this race is an all out sprint from start to finish. It's a strength over endurance race where the strongest legs have the advantage. Good starts are crucial since there are not enough laps to recover from a bad position. Most false starts occur in the 500m. The skaters' anticipation of that crucial good start throws them off before the starting gun is fired.
1000 meters: In this 9 lap race, strategy becomes important. Skaters must position and pace themselves to be in a good place to take the lead in the final laps. If a skater gets too far behind the lead, they won't have time to make a pass all the way to the front in the final laps. The last few laps turn into a full out sprint to the finish line.
1500 meters: At this longer distance, 13½ laps are required to finish the race. The 1500m consists of six skaters per heat instead of four skaters like 500m or 1000m. Strategy at longer distances takes on a whole new level. Most races start out slow and pick up as race goes on. However, some skaters attempt a fast race from the start in hopes that their stamina will let them stay in front all the way to end. Since the 1500m is raced the first day, some skaters start fast in hopes that the other skaters allow the break away because they'll want to reserve their energy for the next two days.
3000 meters: The 3000m is a test of endurance. It's the last individual race of competition, raced after an entire day of racing the 1000m. The top eight skaters who've skated a final, advance to this grueling 27 lap race. The skaters will start slow and tactically position themselves throughout the race. The race gets faster as remaining laps diminish. Sometimes skaters will make a break, attempting to lap the pack inorder to put enough distance so the race won't come down to a final sprint. Conserving energy is the key. The lead expends more energy than those that draft behind so the lead skaters tries to control the pace to a level that won't burn them out as the pace quickens to a sprint in the final laps.
At the senior level, relay competitions consists of (usually) four teams with four skaters. The men relay is 5000m while the women race 3000m. Each skater from each team must take at least one turn performing a 1½ lap sprint around the track.
The skater will then push off his/her next teammate, transferring the momentum onto the next skater. This continues for a total of 27 laps in the women's relay and 45 laps for the men's. The skaters who are waiting their turn, wait in the center of the track. The final two laps must be completed by the same skater.
The relay is fast and furious. Up to 16 skaters are on the ice and it's a full sprint through the entire relay. Faster teammates make up distance lost by the slower members. It's an exhausting race and endurance is major factor. It's exciting to watch. It's been known for a skater make up 1/2 lap lead in the final 2 laps to win by inches.
Most competitions are individual competitions. The 500, 1000, 1500, and 3000 meter events are raced on an individual level where skaters are racing for their own best times and generating points for themselves, not for the overall team.
Skaters from the same country may end up racing each other for individual medals. The point system for individual competition is: 34 pts for first place, 21 for second, 13 for third, 8 for fourth, 5 for fifth, 3 for sixth, 0 if DQ'd. These points are called Final Points and are used to determine the overall scores. The relay is scored the same way, but these points determine team rankings, not individual.
There is also a team competition where skaters earn points for their team/country. The point system is quite different for this one. In each race first place gets 5 points, 3 points for second place, 2 for third, and 1 for fourth. If a skater is disqualified during the race, they don't get any points for that race.
Races are performed at the typical distances of 500, 1000, and 3000 meters. The team competition does not have a 1500m distance. Relays are also part of the team competition. Here, the first place team receives 10 points, 6 for second, 4 for third, and 2 for fourth. Many times the points from the relay is the determining factor. The team with the most points wins.