Best leveling method?

[Roarey]

They have significantly boosted the xp you can earn via dungeons. You now have the option to do the Daily Roulette through Duty Finder, once per day you obtain extra xp by queuing through it. Both Dungeons and Guild Hests are affected by this change, so it is a good idea while fate grinding to do the daily roulette at least once per cool down period. Even after reaching 50, this is a good source of bonus Gil and Tomes used to buy high level gear.

Also they implemented a weekly event log, similar to your Hunting Log...called Challenge Log. It has various goals you can use to earn xp, all while doing things you normally do anyway by playing.(ie..complete 5 unique fates in unique zones, complete 3 dungeons via duty roulette)
Log Unlock: Challenge Log
Pre-Requirements: Level 15 & must first complete “Call of the Sea”
Entry Quest: Rising to the Challenge
Quest NPC: I’tolwann
Location: Limsa Lominsa Upper Decks – X:11 Y: 10

Combine all this with some fates, and beast man dailies and you will flying up the leveling track.
Good luck and welcome back!