You can either simply collect cards you get as drops, or buy cards from the Priest at the Hub (you should check his stock regularly anyways, to buy the Fool cards).
This list is not mine, simply posting it for reference.
Death - Increases damage, lowers max. HP
Greed - Increases gold dropped by monsters
Hope - Increases max. HP
Justice - After taking more than 10% max. HP damage in one hit, you reflect 33% of incoming melee damage back to the attacker for X sec., 30 sec. cooldown
Strength - Increases crit. chance
The Acrobat - Gain X armor while dodging
The Alchemist - Lowers cooldown of consumables
The Archer - Increases ranged damage
The Beast - Increases armor penetration
The Bishop - Gain X% max HP on crit., 5 sec. cooldown
The Blademaster - +20% crit. damage, regenerate 4% max.HP/sec for 10 sec. after critically striking with "Sword Slash" or "Dash Attack", this effect does not stack but the duration is refreshed if you activate the effect again while its already active
The Cannon - +100% crit. damage for 1 second after hitting an enemy with "Bouncing Betty", this effect's duration is stackable, enemies hit by "Explosive Jump" take 100% more damage for 5 sec.
The Executioner - +X damage against enemies below 50% HP
The Fool - No effect
The Guardian - X% chance to deal X damage after being hit by a melee attacker
The Knight - Increases armor
The Moon - Frost explosion on crit., decreases enemy movement speed by 33%, X damage, 15 sec. cooldown
The Reaper - +5 max. Soul Shards, "Shockwave" deals 10% base damage/Soul Shard spent, Scythe special attacks will refund 33% of all Soul Shards spent
The Rogue - Increases crit. damage
The Runner - Increases movement speed
The Slayer - Gain X% max HP on kill, 15 sec. cooldown
The Sun - Explosion on overkill, X damage, 20 sec. cooldown
The Swashbuckler - +33% attack speed after killing an enemy with "Flurry Attack", this effect does not stack but the duration is refreshed if you activate the effect again while its already active, stuns enemies hit by "Coup de Grace" for 2 sec.
The Tower - Overdrive bar fills faster
The Vampire - Adds life steal with weapons
The Warrior - Increases melee damage
Wildcard - Increases damage by X for each equipped Destiny Card, increases crit. damage by X for each equipped Destiny Card