When you're starting out, just grab some quests, and make sure to follow the main story line quests. Also, grab your class quests along the way (every 5 levels). Hop into fates if you're near one (if it's worth the time and effort, some just take too long to finish). At level 15 you'll unlock the first dungeon which will net you some good exp too. Leves can get you SOME exp, but aren't really worth it compared to leveling crafting classes through them.
Essentially, dabble in a bit of everything (mostly quests) and you'll level up pretty quickly.
edit: Also forgot, your hunt log is another way of getting good chunks.
Edited, Feb 20th 2016 8:05pm by Montsegurnephcreep
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