Unlike a bracketed tournament where players who lose can't play anymore, a ladder system in a competition lets everyone play till the end. Players who consistently win move up the ladder, and vice versa for the players who consistently lose. There are different ways to set up a ladder and some very complicated approaches to ranking, but once the rules are established for how players enter the ladder and move up or down it, the competition is seamless. You can set up a ladder with two different ranking approaches.
Decide how players are initially ranked on the ladder. For example, if the competition leaders already are familiar with the strengths of each player, they can assign the players positions on the ladder to begin the tournament. Another way to begin is a "first come, first placed" approach. As players sign up for the competition, they are placed on the ladder directly below the last person who signed up.
The advantage of the first approach is that it takes the strength of each player into account. As play begins, players who are already near the top of the ladder will play other strong players near the top of the ladder, and many good games will result. In the other scenario, the strengths of the players is scattered through the ladder, resulting in many lopsided games between a very strong player and a very weak player. The advantage of the "first come, first placed" approach, on the other hand, is that it allow the competition to proceed when no one knows how strong the players are. Furthermore, it conveniently places new players as they sign up without having to do any calculating--simply stick them on the bottom rang of the ladder.
Decide how many rungs below or above himself a player can challenge. For example, if you have 20 players, there will be twenty rungs in the ladder. To make it difficult for players to rise rapidly up the ladder or fall quickly down it, make a rule that a player can only challenge another player who is three rungs or fewer above him. But if you want movement along the ladder to fall and rise like the wind, don't have a rule limiting how far from his own rang a player can challenge.
When a player beats an opponent in a rang higher than his, the two players switch rungs. This switching shows the progression of better players up a ladder and worse players down it.
If you don't want players switching rang spots just because one beat the other, assign points to players at the beginning of the tournament. When a player wins, he takes some of the other players points. Let's say player C challenges player A and wins. He has 10 points and player A has 20. Because player C wins, he gets five points from player A. This, it so happens, gives him more points than player B has, with his 12 points. So player C switches spots with player B.
Players cannot continuously refuse challenges from opponents on lower rungs. If they do so, remove that player from the ladder and move everyone else up the ladder one rang.
Give plenty of time for the players to challenge one another and move up or down the ladder. Depending on the nature of the game or sport, the time can span over many months.