
The devs have provided us some lore on this. Basically, a fairly limited subset of the populace has the spiritual strength ("anima") to regularly teleport; that subset just happens to be player character adventurers. Most "normal" people can only teleport very rarely due to a lack of anima. When you arrive, you pay the guard gil for Aetheryte upkeep.
Based on the MSQ and mechanics, we know that because Teleport and Return have you traversing the Lifestream, you need to "lock onto" an Aetheryte as a sort of beacon, so you can only teleport to an Aetheryte to which you've attuned; this is a big part of the Titan part of the MSQ and plays into the HM Primal quests, too. Presumably, you can't teleport in combat because it's a time-consuming ability that requires considerable concentration.
So, I basically play it straight from the mechanics and lore.
I'll confess that I have, for comedy reasons, had L'yhta miss a teleport, appearing near but not at an Aetheryte when she's very flustered, but she can't teleport to any random location intentionally. In terms of tracing teleports, that's something she's been actively researching, but hasn't yet produced a repeatable breakthrough -- which is to say that, if the person running the plot wants to allow it, then she can do it, and if not, then she can't. In RP, L'yhta doesn't try to teleport if there's danger about; the spell leaves you extremely vulnerable for a long duration, and that's just asking for trouble. It's not really a viable escape technique.
EDIT: In terms of how L'yhta uses it day-to-day, she views it as just any other spell, albeit one that costs her gil unless she's teleporting back to Limsa Lominsa (because of her associations with the Maelstrom). She uses her Reaper for short distance travel or if she just wants to go out exploring, her chocobo if she wants to go out for a ride, and the airship if she's feeling cheap, but teleportation is her primary mode of long-distance travel. Then again, she is a highly skilled spellcaster who regularly uses magic, so that works for her conceptually.
Based on the MSQ and mechanics, we know that because Teleport and Return have you traversing the Lifestream, you need to "lock onto" an Aetheryte as a sort of beacon, so you can only teleport to an Aetheryte to which you've attuned; this is a big part of the Titan part of the MSQ and plays into the HM Primal quests, too. Presumably, you can't teleport in combat because it's a time-consuming ability that requires considerable concentration.
So, I basically play it straight from the mechanics and lore.

EDIT: In terms of how L'yhta uses it day-to-day, she views it as just any other spell, albeit one that costs her gil unless she's teleporting back to Limsa Lominsa (because of her associations with the Maelstrom). She uses her Reaper for short distance travel or if she just wants to go out exploring, her chocobo if she wants to go out for a ride, and the airship if she's feeling cheap, but teleportation is her primary mode of long-distance travel. Then again, she is a highly skilled spellcaster who regularly uses magic, so that works for her conceptually.
The Freelance Wizard
Quality RP at low, low prices!
((about me | about L'yhta Mahre | L'yhta's desk | about Mysterium, the Ivory Tower: a heavy RP society of mages))
Quality RP at low, low prices!
((about me | about L'yhta Mahre | L'yhta's desk | about Mysterium, the Ivory Tower: a heavy RP society of mages))