To earn Cups and move up the Leaderboard, you must win ranked games. The number of Cups won per match, is dependent on your current rank, and the rank of your opponent. The higher the rank of your opponent, the more Cups you will win.
On the other hand, the number of Cups you lose also depends on the rank of your opponent. Losing to a player below your rank will cost you more Cups than if you lose to a higher ranked opponent.