An icon on an ability button will indicate if that ability has a buff or debuff; if you mouseover the button, a description will appear in the "More Info" section at the bottom left of your screen.
Most buffs and debuffs last multiple turns. When a buff or debuff is on a character, it will appear at the edge of his/her side of the screen, showing the damage and the countdown of how many more turns it will last, if appropriate.
Damage
Countdown
Damage from debuffs is not mitigated by resistance. For example, Dark Magic resistance may reduce the initial damage of a poison dark attack, but it will not reduce the poison damage from the debuff that ability cast.
Characters that are switched out will continue to take damage from debuffs, and even die while out of combat. Buff and Debuff icons appear on top of the deck cards.
View a complete list of buff and debuff icons.