Summary of the most useful information I found in the comments:
1. Use the quest item ("Fistful of Feathers") at a summoning circle in the southern Arrakoa village
2. A grey bird will be summoned and follow you around (like a pet) and you'll receive a buff called "Lashh'an Channeling"
3. Do NOT mount to prevent it from bugging / despawning
4. Walk back to Sylvanaar (the Alliance base to the north) with the bird still following you
5. As soon as you come close to the NPC, Daranelle, the quest objective will be completed. She's at the right side of the road as you enter Sylvanaar, after the crossing and hidden behind a small hill if you're walking through the main "gate".
PS: Do not dawdle while the bird is following you, it will despawn after 10 minutes and you'll have to summon it again.