Try to win each round with as few cards as possible, and this also chains into how to develop your deck when collecting cards for your 'Units' try to only have cards with very high point values so that you don't need many for a very high points score in a round. If you empty your deck in the first round and win but your opponent has at least two unit cards left at that time, he can simply put down one unit card each in the following two rounds to beat you.
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Unless you have the special abilities of the Northern Kingdoms, Monsters factions or a spy card, your 10 cards is all you have for your full three rounds and you discard everything played after each round, so make sure to plan for the long game.Even if you had a higher points score when you 'Passed', your opponent could easily keep putting down cards to surpass you and win the round. When you 'Pass', you will not be allowed to put down any more cards for the remainder of that round, no matter how many your opponent puts down afterwards. Be very careful of when you choose to 'Pass' in a round if your opponent has not.
A draw makes both players lose a point unless you are the Nilfgaardian Empire. Losing a round loses you one of the points, if you lose both you lose the match. This is represented by the Round Points, or red gems, next to each player's name.