Each Teleport spell is trained at a portal trainer, who is usually located near the mage trainers in a major city. In Shattrath the neutral portal trainer, Iorioa, is located in the center of the city, near the various city portals. In Darnassus the portal trainer is located in The Temple of the Moon.
The mage will appear in the capital city near the portal trainer of that city. In Stormwind, for example, players appear inside the mage tower at the center of the Mage Quarter. This is the same location as is used by the mage Portal spells, and the Portals from Shattrath and Dalaran.
Ancient Teleport: Dalaran will port the mage to Dalaran Crater, but the player will fall approximately 150 feet, and without a slowing effect the player will take damage.
Mages cannot learn the teleport spells of the opposing faction.