Leagues generally last 3 or 4 weeks. When you join a league you are given 5 packs of cards and several base buildings for each domain. You can then make an Army from these cards. The only requirement is that you have at least 25 cards in your League Army. You can have more than 3 of a particular card in a league Army if you were lucky enough to get them in your League collection.
You can build any number of armies from your league collection and you can change your armies at any point.
Once you have constructed your army you save it and return to the player list screen. Then you select the Army you want to use from the drop down. You will be randomly assigned to play anyone else who is also wanting to play a league game.
Each week in the league you can play a certain number of games usually around 8. You can play a particular person no more than 2 times. And the end of the week you will get a new pack of cards added to your collection. You can then improve your league Armies.
You get 3 points for any game you win in the League and 1 point for any game you lose. After you have played your games for the week you can still play a few tiebreaker games. You get 1 tiebreaker point for a win and -1 tiebreaker point for a loss.
Prizes in Leagues: Leagues have an entry fee to join. When the league is over all the entry fees minus 10% are collected into the "prize pool". So if the entry fee was 10 gold and 50 people joined the league the prize pool would be 450 gold. This prize pool is divided among the top finishers of the league.
These are like normal leagues except you only get 3 packs to start with. You pick a certain domain you want to play and all your packs will be made up of cards from that domain.