How do poison counters work? What are the scenarios a player would receive a poison counter?
All you really need to know is that you lose the game if you get 10, and that they're nearly impossible to remove. Generally if you see a card that talks about poison counters, it'll be a card that gives them, so this should never really be confusing - if the cards don't mention them, you don't have to worry about them.
By far the main way to get poison counters is from creatures with Infect, like Blighted Agent:
Infect (This creature deals damage to creatures in the form of -1/-1 counters and to players in the form of poison counters.)
There's was also an ability called Poisonous, but it's only on a couple cards. Virulent Sliver gives all Slivers Poisonous 1:
All Sliver creatures have poisonous 1. (Whenever a Sliver deals combat damage to a player, that player gets a poison counter. A player with ten or more poison counters loses the game.)
There are several more cards that just explicitly give a player poison counters.