Well first of all, many alchemists I see in the server does not have any specializations:(. These specializations are
Potion master, Elixir master, and transmutation master. All of them allows you to have a CHANCE at getting more than what is stated during their respective creations.

For example, transmutation master can allow truegold transmute to up to 2 or 3 truegold while using only the materials of one. However, note that the chance of it happening is quite minimal and personally, after about 30 truegold transmute, I only got 2x three TG and 4x two TG.

At the moment, these quest are not updated to be on par with the cataclysm items. Therefore many think that the quest is bugged, but the outlands version (TBC?) is still working.

You can get the starting quest at Alchemist Gribble (alliance) or Apothecary Antonivich (horde)

The quest should be this .

Although the quest will autocomplete after you selected a alchemy mastery, do not proceed to Zarevhi yet, as he will demand for 4 primal mights for completion.

These goes for about 12k (sarg) on the AH each, and 4 of them burns quite a hole in your pocket. Fret not! As a alchemist like yourself can transmute primal mights too. You can probably find the recipe on the AH that are totally overpriced as it is quite a limited item, but you can and should buy from these NPCs at only 8g each.

After that, just farm up 40 of each mote (Earth, Fire, Air, Water, Mana), get your primal mights and enjoy the specialization!

NOTE: In the soon coming patch of 4.1, in retail this quest is updated to require 4 truegolds instead of 4 primal mights. Depending on your server, truegold might be easier and cheaper to acquire than primal might, so you might want to wait for the patch to hit before you do the specialization.:D