Lots of poisons actually work because they act like a vital chemical but lack it's fuction.
Lets take black widow venom.
And you see her venom is highly neurotoxic
Which is to say that it attacks the central nervous system
Causing intense pain
Profuse sweating
Difficulty in breathing
Loss of consciousness
Violent convulsions
And finally death.
It works by fitting into the same "key" as our normal neuro transmitters.
Except it sends a totally different signal, or none at all. Causing all kinds of nasty effects.
Others are more acids, simply dissolving the cells.
Others are signal peptides that bind to the surface of a cell and pretends to be a signal peptide to induce a harmful effect, such as apoptosis (controlled cell death, aka cell-suicide)
The reason these vemon's or poisons don't hurt the creature it self is because they're produced inside glands, that keep them away from their target tissue.
Edit:
Bonus Internet Points for anyone catching the reference.