You have 6 cards in your deck and you can place up to 3 cards on the field.
Each card costs different amounts of elixir. Each player starts with three elixir and they get one more every turn so the next turn each player will have four. The max will be 10 and at that point every turn will be 10 elixir.
This is where you battle other players to win chests and trophies. Every once and a while there will be a tournament that has prizes. The higher up you go you will go up to a higher arena which has better chests. There are trainers you can fight to gain gold and wooden chests(worst chests).