The best way to level any DoH is:
1. Always craft HQ - you will want to have them all DoH classes for the cross class abilities to make HQ craft much easier.
2. Complete your crafting log, each first completion grants a bonus.
3. Completing Leve Quest turn ins. Turning HQ doubles the Leve reward.
Up to 50, there is always a turn in, that only requires you to make 1 item, and the reward is pretty decent (not the best). This leve is issued in town and handing in to another person in town.
Using Gridania Leves
Speak to Gontrant and the quest which is turned in to Maisenta. She is just over by the aetheryte. Ususally takes about 3 or 4 leves for each level up. This approach saves you time, you can craft a bunch, and just run back and forth turnin, then restart leve.

Now, if you have a lot of playing time and are burning through you leves to quickly using the above approach, you can opt to use the Triple turn-in Leves. Each Leve tier has one Leve that usually the small XP listed but you can turn in that Leve 3 times and it only cost 1 Leve quest.

4. Join a Grand Company and deliver request DoH items each day.
5. Do the Ixali beast tribe quests, it specifically geared towards DoH players.