If a creature with toxic deals combat damage to a creature or planeswalker, or if it deals noncombat damage, toxic has no effect and no player gets poison counters.

Toxic doesn't change the amount of combat damage a creature deals. For example, if a 2/2 creature with toxic 1 deals combat damage to a player, that creature will deal 2 damage. The results of that damage are the player loses 2 life and gets a poison counter.

Any other effects of that damage, such as life gain from lifelink, still apply.

Conversely, replacement effects that apply to the number of counters put on a player can modify the counters placed this way. For example, Vorinclex, Monstrous Raider's last two abilities can apply to counters placed this way.

The bonus Vishgraz receives due to its last ability may cause it to survive combat damage in some cases. For example, if an attacking Vishgraz is blocked by a 3/3 and another creature with toxic 1 is attacking at the same time and is unblocked, Vishgraz with deal 3 damage, receive 3 damage, and get +1/+1 at exactly the same time. The end result is that it will stay alive and be a 4/4 creature with 3 damage marked on it.

Damage dealt by a creature with toxic grants the same number of counters regardless of how much damage is dealt. Notably, if a replacement effect modifies the damage in some way (such as that of Gratuitous Violence), the number of counters given remains unchanged.

A player with ten or more poison counters loses the game. This is a state-based action and doesn't use the stack. In other words, it happens immediately and players can't respond to it, just like a player losing the game due to having 0 or less life.

Multiple instances of toxic are cumulative. For example, if a creature has toxic 2 and gains toxic 1 due to another effect, combat damage that creature deals to a player will cause that player to get 3 poison counters.