Okay, since there seems to be a lot of confusion about how to spec into Gnomish/Goblin Engineering AFTER you have unlearned engineering and pick it up again, heres how it goes.
You must level your Engineering Skill up to 225.
When you have made your decision, go to Tanaris and head east out of Gadgetzan.
When you reach "Steamwheedle Port" head north, and just outside of town there is a small hut,
kind of 'magical' looking, inside you will find a Gnome, wearing a purple turban and a table with a book on top of it.
Right click on the book "Soothesaying for Dummies" and select one of the two options.
(something along the lines of..)
1. "I am absolutely sure I wish to specialize in Goblin Engineering."
2. "I am absolutely sure I wish to specialize in Gnomish Engineering."
You will see a message saying "You have learned a new skill: (Gnomish/Goblin) Engineering
Done!
Happy Trails,
Gorelash.
Source:
http://www.wowhead.com/quest=3635/gn...nts:id=1565094