You can earn extra cards by purchasing them from the
market or, as you say, waiting for a booster drop. The higher your level, the higher your chance of receiving one (eligibility is defined by having used up all of your drops for a given title), though Valve claims that the frequency of booster drops in general is determined by the community's overall badge crafting rate. Also, for F2P games in particular, you can earn more drops by spending approximately $10 in-game.
There's an FAQ you can sift through for more details.