At level 20, Alliance characters train poisons with a quest from the SI-7 operatives in the Stormwind Barracks. Horde characters can get this quest by speaking with the rogue trainer in the Cleft of Shadows in Orgrimmar. Note that in order to complete the quest, you need to have around 85-90 skill in lockpicking. I would suggest getting it up to 100 before giving the quest a whirl.
Horde Starting Quest,
http://www.wowhead.com/?quest=2480
Also, Thanzil's disease that you can can be cured really easy without the boring time consuming quest.
-----Pinched from Elitism on Thottbot:----
I figured I'd write a thorough quest description for alliance rogues .. so here goes!
1) Get the quest "Mathias and the Defias" from "Master Mathias Shaw" at SI:7 in Stormwind City (75,59)
2) Travel to Westfall. Head to the tower in the south east corner. Just north of the tower you'll find Agent Kearnen hidden (68,71). She will give you the quest "Klaven's Tower".
3) Next you'll need to grab the key from the "Malformed Defias Drone" roaming around the tower. As I didnt have distract at the time of doing this (was only lvl 20) I found the only way I could do it was to wait till he turns around down by the campfire near the water. You have a split second to pick pocket him. If you fail, just gouge him, run out of range and try again.
4) Next head to the top of tower. You can do this without aggroing any mobs if you just have a little patience. When you get to the top, sap "Klaven Mortwake", open chest (requires lockpicking - I had 100 in skill) and get out of there fast. After opening the chest you'll have a debuff on you called "Touch of Zanzil" which will be dealth with later on.
--SNIP--
Just find a druid to sort out that debuff... or wait a week
wowhead ftw :P