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.
Mages cannot learn the teleport spells of the opposing faction.
Teleport cannot be cast in combat.
Tips and tactics
A flight to Shattrath City from any point in Outland is always more expensive than the price of a Rune of Teleportation. Thus, from any place in Azeroth or Outland, it is always faster and cheaper to teleport than fly to a city. Same applies in Northrend and Dalaran.