Mostly tournament wins, but also league wins/high placings. A few other pvp events (I think just winning War atm) also give them. You'll get a PM on the forum with a code that you then paste into the reward code box after you open it up.
Marks can indeed be used in non-pvp games. They can also be upgraded like any other card, but most people don't do that.
After entering the code, the screen looks like this and you pick your reward:
(That code was valid once, but it won't work anymore, because it's been cashed in :p I left it just as an example of what it would look like)
