Elf Introduction 1-5
1) When you enter the gameworld accept Merethen's Quest.
2) With the quest in hand follow the path southwest to Dorongur Whitethorn. Refresh your quest at him and talk to your trainer in town. After you do that talk to Dorongur again and refresh your quest. Accept all of the other quests that pop up in town.
3) Head west of town and kill 6 Lynx's for their pelts. You can find a lot of Lynx's around the frozen lakes.
4) Once you're done with the Lynx's head to Elladan and refresh your quest. With new quest in hand head north to the mines entrance.
5) On your way to the Mines entrance kill Cave Claws. Finish off any Cave claws you need as well once you get inside of the mine.
6) Search all 4 of the Dead Goblin bodies while working your way to the back of the mine.
7) At the back of the mine you'll find rubble that you can loot for "The Lost Lore of Edhelion"
8) Once you're done that quest exit the mine and refresh your quest at Elladan. Then return to town and turn in all of your quests. From town head west to Frerin's Court. Refresh your quest at Dwalin. More quests will pop up in town, accept them.
You should now have:
9) With all of these quests in hand head west of town and kill Aurochs for their meat, A Goblin to search and Frostmantle. Once you've completed all of these return to Frerin's Court and refresh your quest.
10) Follow the path west and accept the quest from Erynwen. Continue west along the path until you reach Goblins.
11) Once you start seeing the goblins keep an eye out for Skorgrim's Bloom. You have to destroy 6 of these. Once you've destroyed all 6 enter the mine at the top of the path.
12) Clear your way to the back of the cave where you'll find Elrohir. Continue your quest at him and then exit the cave. (If you jump off the side you will survive, just have a debuff that slows your movement speed.) Return to Erynwen and turn in your quest. Then continue to Frerin's Court and turn in your quest to Dwalin. Make sure you're done every quest here and then talk to Dwalin and tell him you're ready.
Elf Intro Instance 5-6
1) Once you enter the instance speak with Dwalin and continue your quest. Follow him through this tunnel killing anything that attacks him until you reach the water part.
2) What I mean by the water part is when Dwalin asks you to collect water for him from a bucket. Run behind him and grab water from the bucket and run back towards the fire. You'll automatically throw water on the fire. After you do this kill the goblins that attack him. Continue to follow Dwalin and protect him. Eventually you'll come to a gate, and when Dwalin opens it you'll kill Gormr. After that Dwalin will sit down.
3) Talk to Dwalin and tell him you're ready to continue. You'll come out into a large room, kill Dwalins attackers then follow him up the staircase. Watch the quick scene and kill Marrer and the Goblin Chief. Untie the elf thats tied up and talk to Dwalin again and tell him you're ready to continue.