You can unlock specializations for your character that further refine your character. Mage, Warrior and Rogue each has three specializations.
Mage
-Knight Enchanter
-Rift Mage
-Necromancer
Rogue
-Assassin
-Artificer
-Tempest
Warrior
-Champion
-Reaver
-Templar
You will unlock a mission on the war table a while after you reach Skyhold about getting trainers. It's an instant mission, do it and the trainers will arrive in Skyhold. You can talk to them and you will get a short mission chain for each possible specialization. It's up to you if you want to do all three or just your chosen specialization. If you do all three you still have to choose just one specialization in the end. It will then appear in your character record and you can start allocating points. Remember that the smith in Skyhold sells respec potions! If you wish you can reallocate points and move them all over to your specialization right away.
Human, Elf and Qunari can be any class, but Dwarves can not be mages.