Only lower-ranked players can issue a challenge (No. 8 can challenge No. 7, but 7 can't challenge 8). Challenge rules usually prohibit the challenged player from declining to play; if you are challenged by a lower-ranked player, you have to accept. Typically, the lower-ranked golfer is limited to challenging the players who are, at most, up to three spots above on the "ladder."
In order to keep the tournament moving, a time limit for playing agreed-upon matches is a good idea; playing within one week of a challenge is common. Use full handicaps.
If the challenging player wins, he moves up the ladder, trading places with the golfer he beat. If the golfer who accepted the challenge wins, he maintains his position on the ladder.
The object of a ladder tournament is to move up the ladder; the player at the top at the end of the tournament period is the winner.
Ladder tournaments obviously take time to play. When might a ladder tournament be used? Let's say the Anytown Country Club Men's Golf Association issues its summer schedule, with other kinds of tournaments scheduled from June through August. That 3-month period is an opportunity to schedule a concurrent ladder tournament, running throughout the summer.

