There's a levequest dealer available every five levels. It's just a matter of finding them (Most require you to 'unlock' them by doing a trial levequest as a battle class first, as mentioned)

Anyway, people did FATE trains in 2.0 because it was almost the only way to level. Since then, however, EXP gains were massively improved from other sources to be on par. The fastest source of EXP in the game is the Low Level Duty Roulette, which you can do once per day and you can expect to get at least one level from. Dungeon EXP in general has skyrocketed and is the most effective way when you can get in.

If you miss the days of FATE trains though you can sometimes find groups in Coerthas or North Than at high levels still. Or Western La Noscea for the 10-20 range simply because of how convenient it is; there's almost always people there.