Increasing your character's skill and attribute ratings through training is the primary way to gain an advantage over your opponents. Even if your deck is full of high-value cards, low skill ratings will result in lost battles.
Training is done through skill points. Winning a battle in a tournament or in random combat will award you skill points. You can spend a skill point to gain a 0.1% gain in a skill.
Battles against live players within certain range of your battle rating awards you skill points (3 if you win, 1 if you lose). This way, you should never quit a battle even if you are losing, since you will miss out on a skill point reward!
Attributes will be trained through your cell phone (or another means if you don't have a cell phone). This is under development, so stay tuned.