At level 7 and then level 14 you will be given the chance to learn specilizations (you will gain a "specialization point" at those levels and it will stay with you through subsequent levels until you spend it.) However, first you must find their trainers and convince them to teach you - or find a book that will teach you. You can "learn" specializations for classes other than your main character's. Once you unlock a specialization it stays unlocked for all the characters on your profile (and all party members on all your characters.) The specilizations and the ways to get them are listed below:
Berserker: Oghren can teach you if your approval is high enough or you can learn from Gorim at the Denerim Market.
Champion: At the very end of "The Urn of Sacred Ashes" questline you will learn this from Arl Eamon.
Reaver: You can learn from Kolgrim at the Wyrmling Lair (he is a member of the Cult of Andraste - the one you meet when you do the Sacreligious and/or Ceremonialist achievments)
Templar: You can learn this from Alistair if you approval is high enough - or you can buy the book from Bodahn in the Party Camp.
Ranger: You can buy the book from Bodahn in the Party Camp.
Bard: You can learn from Leliana if your approval is high enough or from Alimar in Orzammar.
Duelist: You can learn from Isabella at "The Pearl" in Denerim.
Assassin: You can learn from Zevran if your approval is high enough or in Alarith's Store (after "The Landsmeet" questline has started.)
Blood Mage: You can learn this from the desire demon in the fade (in the "Arl of Redcliffe" questline.)
Arcane Warrior: You can learn this from The Presence at the Brecilian Ruins (in the "Nature of the Beast" questline.)
Shapeshifter: You can learn this from Morrigan if your approval is high enough or from Varathorn at the Dalish Camp.
Spirit Healer: You can learn this from Wynn if your approval is high enough, buy the book at the "Wonders of Thedas" shop in the Denerim Market (the same one where you can usually buy a tome for the Educated achievment) or if you have the Warden's Keep DLC you can purchase the book from a trader in the Keep after completing the questline.