Where byes come from
Six teams do not fill a bracket of eight. That leaves two empty slots, so two teams skip round 1. Eleven teams in a bracket of sixteen leave five byes. The number of byes is always the next power of two minus the number of teams.
Why the top seeds
Seeding ranks the teams by strength before play. The reward for a good seed is an easier road, and a bye is the easiest road: a free win. A team with a bye still has to win every game after it, so it plays one game fewer than the teams that started in round 1.
How seeds are placed
Seeds go in the bracket so that seed 1 can only meet seed 2 in the final, seeds 1 to 4 can only meet in the semifinals, and so on. In an 8-slot bracket the first-round pairs are 1 against 8, 4 against 5, 2 against 7 and 3 against 6. Byes simply replace the weakest seeds in those pairs, which is why seeds 1 and 2 are the ones skipping round 1 in a 6-team bracket.
No rankings yet
If you have no ranking, draw the seeds at random. A random draw is fair because nobody had an edge, but it does mean the byes can land on a weak team. For leagues, seed by last season or by the round-robin standings.
Questions
Can I give the byes by lottery instead?
You can, and some casual events do. You lose the main benefit of seeding, which is keeping the strongest teams apart.
What if two teams are tied for the last bye?
Break the tie with last meeting, then a coin flip. Decide before the draw, not after.