When your skill has progressed to 200 and you are level 30 or higher, you will be able to start your specialization quest.
See an artisan trainer in the Undercity, Ironforge, Ratchet or Shattrath for it. You will receive a book with some information about both Goblin and Gnomish engineering, which amounts to: Goblin engineering focuses on dealing damage through their creations while Gnomish engineers craft devices with more subtle effects. (Mind control, debuffs, root, etc)
If you wish to go the way of the Goblin, both Alliance and Horde players need to visit Nixx Sprocketspring in Gadgetzan.
For Gnomish Engineering, Alliance visits Tinkmaster Overspark in Ironforge, while Horde goes to Oglethorpe Obnoticus in Booty Bay.
Before making your trip over, you may want to finish reading this chapter and create the required items beforehand.
Once you complete either the gnomish or goblin version of the ’The Pledge of Secrecy’ quest, your specialization will be decided. It is impossible to go back and change your specialization afterwards, so make sure you are certain of your choice in advance!
Put your specialization choice off a while if you can’t decide. You can become a 300 expert engineer without picking either gnomish or goblin engineering easily. Not being specialized does not hurt your skillup speed, but you do miss out on some gadgets by waiting. If you aren’t sure what to pick, I’d still recommend you wait until you are.
To help you decide, check out the gnomish and goblin engineering schematics chapter.

Take note of which schematics produce a Bind on Equip item. Being a Gnomish engineer doesn’t mean you cannot use any Goblin engineered creations, and vice-versa.

Show Your Work
Regardless of which path you decide to take, you will have to complete this quest after signing your specialization’s charter. For both specializations, it involves making a bunch of stuff and handing it over to your respective gnomish or goblin specialist.
For the Goblin version you need to produce: 6x Mithril Tube, 2x Advanced Target Dummy and 1x Accurate Scope.
For the Gnomish version you need to produce: 20x Big Iron Bomb, 5x Explosive Sheep and 20x Solid Dynamite.
When you finish this quest, you will receive your membership card. It stays valid for 1 week of playtime. (168 hours worth of playing) It’s not uncommon for someone to have learned all of his/her specializations schematics before the card runs out for the first time.
Refreshing your membership card will net you a gift in the mail. The gift is usually components or bombs. There is a small chance that you will get a special schematic for your specialization. For Gnomish engi’s it’s Lil’Smokey, for Goblins it’s a Pet Bombling. Both are non-combat pets.