You increase your Player Level by collecting XP. Once you have collected enough you will level up, your XP will return to 0 and any additional XP you have (over the required amount) gets added to the new XP total you need to level up again.
There are two ways you collect XP, the first is by upgrading the cards in your collection. The higher the level of the card when it is upgraded, the more XP it will give you. The second way to get XP is by completing your Daily Missions. You get a new one every day and when completed rewards you with XP, and other great stuff.