You cannot make a poison potion in Minecraft without using a brewing stand
Craft a brewing stand using 1 blaze rod and 3 cobblestone or blackstone
Place the brewing stand and add blaze powder as fuel
Put water bottles in the bottom slots of the brewing stand
Add nether wart to make awkward potions
Add a spider eye to the awkward potion to make a potion of poison
Add redstone to extend the poison duration
Add gunpowder to make a splash potion of poison
Add dragon’s breath to make a lingering potion of poison