To participate in duels, tap the Tournament of Fame icon in the lower left corner of the Faction Wars menu.
At the end of the season, players will receive rewards based on their position in the leaderboard. The season timer can be found at the top of the screen in the Faction Wars section.
Note that there are 2 timers in Faction Wars mode: the dueling season timer (in the Top 100 section) and the Faction Stage timer (in the main Faction Wars section).