Poison is simple enough to understand. It works to slowly eat away at your opponent's life points. The damage is based on two things:
First is that the character that has it wins the round and inflict damage on the player. If it does not win the round, then it is defeated and the poison is not activated. If it does win then...
Onto point two. If your character defeats the other character then inflicts damage, afterwards the set amount of damage that it states on the card (like 2 or 3) it inflicts that amount of damage after every round afterwards. There are limits of how good the poison is and also how long it lasts. If it says (for example) poison 2, min 5, then that means the poison shall continue to inflict poison to the person's life points until it reaches five. After that, the poison just stops inflicting damage.
Here's an example Sheitane wins the first round and has 2 min 1, if no one else does damage she will do a total of 7 damage. 1, 2, 2, 2. If she hits the third round she only does 3. 0, 0, 1, 2. One of the quirks with many poison characters is rather then high power they do high damage so they hit the min pretty fast like Crassus. Nice thing is though if he just gets SoA'ed then he'll still do 9 damage hitting first round. Also a wierd quirk is if you hit min then gain life the poison doesn't start again. Not sure if that is a bug or intentual.