The usual order
- Wins (a draw counts half a win).
- Head to head: the result of the game between the tied teams.
- Point difference over the whole event.
- Points scored over the whole event.
- A coin flip, or a playoff game if the result matters.
Three teams tied
Head to head only works between two teams. With three tied, look at the games among those three only. If one team beat both others, it is first. If each beat one, the head-to-head step is tied, so move on to point difference. If a head-to-head step splits the group so that two teams are still level, those two go back to head to head.
Point difference
Point difference rewards teams that win big, which can encourage running up the score. Cap it per game (many events use 5 to 8 points) and say so in the rules.
Soccer-style points
Soccer awards 3 points for a win and 1 for a draw. That changes the table: two draws and a loss (2 points) is worse than a win and two losses (3 points), where half-point scoring would call them level. If your league uses 3-1-0, say that, and use it for the whole event.
Questions
Which tiebreaker do most leagues use first?
Head to head, because it is easy to explain. Point difference comes next.