You first have to get a referral from an engineering trainer in a capitol city. Remember, you do have to have 200 skill, and be at least level 30 to be eligible.
Having done that, you are issued your [Goblin Engineer Membership Card], which entitles you to training on the 'goblin engineer only' engineering recipes. Congratulations! You have specialized in Goblin Engineering!
Your membership card
Prior to the release of Wrath of the Lich King, having completed the exercises above, you were given a [Goblin Engineer Membership Card]. It remained valid for 14 days of 'played time', not 14 real days.
If you ever found yourself without this card, you could pay 2 gold in dues to the Goblin Engineering trainer (still Nixx Sprocketspring) and get a new one. Since the release of Wrath of the Lich King, Goblin Engineering is added to your book as a skill.
An added benefit of renewing your membership prior to patch 3.2.2 was that you would be sent a renewal gift of some useful engineering schematic. [Schematic: Pet Bombling] formerly could only be acquired this way. However, this item now drops in Gnomeregan.
Goblin Engineering items
Goblin Engineering items require specialization in Goblin Engineering to craft.
Since patch 3.2.0, Gnomish Engineers and Goblin Engineers can now switch profession specializations for a fee.
You can now switch specializations by visiting Narain Soothfancy in north east Tanaris. The book on the table in his hut will allow you to switch specializations for a fee of 150g.
"Your want to know about goblin Engineering? Try asking one of their best and brightest engineers about it - I think his name is 'Nubby Stumpfingers.' Want to know why he's named that? THAT'S Goblin Engineering." — Ringo Tragediction, Gnome Engineer
"Say what you want about us Goblins, but I will tell you this: WE HAVE EXPLOSIVES!" — Yazz Nitrospork, Goblin Bombardier