Esrim's spirit will take off immediately over the bridge when you get this quest. Follow it!
If you miss running after his spirit right away then speak to him again and it should cause it to restart.
Follow his spirit across the bridge and along the path.
Two Zek bouncers spawn and will attack. Kill them.
He will then teleport you to the opposite side of the mountain you're on and take off again right away. He headed northwest toward a rock across the river at ( -607, -5, 239 ) /waypoint -607, -5, 239 and was attacked by a capricious razorclaw.
He then will head north (you'll likely have to kill normal aggro mobs that attack him here) until he reaches ( -647, 9, 81 ) /waypoint -647, 9, 81.