Equip poisons in one of your activatable (sp?) slots, on the bottom left corner of your armor slots in your inventory. To use them, right-click on one and select "use." A poison icon will appear in your buff window. Most will last for 12 hours or 100 procs, and they'll go away if you die. Poison bottles have several charges, so one can last you quite a while.
If you are a rogue or predator, you can start using poisons at level 10. Many suburbs have alchemy stores that sell lower-level poisons, but these will be useless by 20. There is a poison store in South Qeynos (clearly marked on the map), and I'm sure there's an equivalent one in Freeport, but I'm not sure where. These stores sell poisons for many level ranges. You can also buy them from the broker, if someone is selling poisons in your level range. There are some NPC sellers in adventure zones who just sell one or two types of poisons (player-made poisons are better though).