Depending on the type of game, victory is achieved by the first player to collect a certain number of VP:
Classic: 20 VP (25-35min)
Extended: 30 VP (35-45min)
Alternately, the winner is the first player to accumulate a total of 30 XP.
You always get 1XP at the start of each of your turns regardless of the contribution of your champions.
Being the first player to have all their Champions downed.
Being the player with no more cards to draw.
The most important source of VP comes from unblocked attacks. You can also get some VP in a number of other ways, for example by completing campaign card objectives.
The most important source of XP, comes from your champions. You can also get some XP in various other ways, for example by destroying enemy allies and minions.