I'm ace at Gwent and I love it as much as the main game itself so I'll chime in.
Essentially you play the opponent. Pay attention to the deck they have. E.g if it's nilfgaard, then they'll probably have loads of spy cards (which let them draw more cards). So you'll want to use your own and some decoy cards to claim theirs in the first round.
But yeah, it's best out of 3. The trick is that sometimes surrendering a round is the smart thing to do. If you go all guns blazing determined to win at all costs then you may win a round but have no cards left to win the 2nd round like you need to. That's why I mentioned nilfgaard decks. They generally surrender the first round to just accumulate more cards for the next 2. Whereas Monster decks will usually go all guns blazing for the first round.
Other than some special cards and abilities, you don't draw more than the 10 you have at the beginning. So just try and use the minimum necessary to win a round, keeping in mind that you have another round to win. You can challenge almost every major npc and trader, innkeeper etc to a game. Winning rewards you with a card. The Gwent questlines give great cards as rewards also.
It's worth getting to understand it as it's probably the best game within a game I've ever played. It's easy to understand and you'll get the hang of it after a few rounds. But the Ai is really good and human like so it will provide a fun and sometimes challenging extra thing to do throughout the game