Poisoned apples are unfortunately very tricky to use effectively. I've only gotten it to work once and it was more trouble than it was worth. In order for an NPC to eat a poisoned apple, that apple has to be the ONLY available food source in the entire cell. That means you must search every container and check plates/bowls/etc for any foods and withdraw them into your inventory. After that, place the poisoned apple in one of the containers that typically contains food, wait for the NPC's schedule to tell them they need to eat, and as long as there are no other options, the NPC should take out the poisoned apple, sit down, eat it, and then die a few seconds later.
EDIT: Oh yeah, as stated below, you can also just reverse-pickpocket it into their inventories. That works too, but I'm pretty sure it doesn't speed anything up. And from a roleplaying perspective, suddenly finding an apple in their inventory should make that NPC pretty suspicious!