For this trophy you have to successfully poison either a portion of food or drink, your victim then has to consume the spiked substance leading to either a fatality or they will have a sudden urge to go to the toilet. Once the effects kick in, the trophy will pop.
When you are planning on poisoning someone you have to pick up the actual Poison. Usually it is conveniently placed near the actual item of food or drink that you intend to spike. Once the Poison has been found, find something to poison with it and the game will prompt you to Poison it by pressing . Make sure no one is around, otherwise your cover will be blown and as a result it will prevent your victim from sampling the poisoned item. Furthermore if you blow your cover by going in all guns blazing then try to spike the food/drink, due to your aggressive manor the victim will be on high alert and therefore will be less likely to sample the poisoned concoction.
Technically speaking it is possible to complete the game without poisoning anyone but that is only the case if you play the game aggressively. If played stealthily, then poisoning targets etc does make life easier and ideal but the first real opportunity is in Mission 3: The Bjarkhov Bomb – see the Professional Difficulty, Silent Assassin and Weapons Guide on how to Poison someone in that particular level.