As stated above, make sure to unlock 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