Dwarf Intro 1-5
1) When you exit the instance accept the quest from Bolli and head up the staircase to his right. At the end of the ledge you'll see Dori. Refresh your quest at him then find your trainer and speak with him. Continue your quest at the trainer and train your skills. Then return to Dori. Continue your quest at Dori and accept the other quests that pop up in Berghold.
2) Head out of town to the north and over to Selur. Accept his quest then head north towards Silver Deep Mine, but kill 6 Lynx's for their pelts on your way. After you've collected all 6 Lynx pelts head into the Silver Deep Mine. (It's where the tutorial was if you're confused on its location.
3) Once you're in the mine kill 6 Cave-Claws. After you've killed all 6 head to the far back of the mine where you seen the troll get turned to stone earlier. Loot the Edhelion scrolls from the rubble in the room in front of the troll.
4) Once you have the scrolls exit the cave and return to Selur. Turn in your quest then continue south to Berghold. Refresh your quests here then head northwest to Frerin's Court which is in the center of the map. At the far western end of that you'll find the Guardhouse (Look at your mini map for the ring outside of a building).
5) Once you're inside the building refresh your quest at Olin who's in the back of the building. After you refresh your quest head far east to Rock Belly Pit. To get there run east from Frerin's Court to the Crossroads (Look at my picture). At the Crossroads follow the path up the mountain side, once you're up the mountain side head south to Rock Belly Pit.
6) Inside Rock Belly Pit you'll want to collect 4 Nestedelais. Once you have all 4 exit the pit and head back to Frerin's Court. Return to Olin and refresh your quest. Head out of the guardhouse and east to Dwalin
7) At Dwalin refresh your quest, and grab the other quests that pop up in town.
You should now have:
Intro: Goblin Prowlers
Stocking the Larder
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.
Dwarf 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.