1 - Refuge of Edhelion
5 - Frostmantle
2 - Elf Encampment
6 - Erynwen
3 - Deep Silver Mine
7 - Axe-Head Path
4 - Frerin's Court
8 - Goblin Cave
You are back to Refuge of Edhelion (1). Talk to Merethen. She'll tell you to find Dorongur Whitethorn. Head east and go to elf encampment in Thorin's Gate (2). Talk to Dorongur for some gold and probably advancement to level 2. He wants you to speak with your class trainer. He can be found right in the encampment. Use this opportunity to train the only skill that is available for now - remember to drag&drop it into the quicklaunch bar at the bottom of the screen. Speak with Dorongur once more to get your reward and another quest - he wants you to go to Deep Silver Mine and talk to Elladan (3). Before you go, get two more quests from the camp. Talk to Gailthin (Lost Lore of Edhelion), Orodlin (kill 6 cave-claws), and Laergil (get 6 lynx pelts). When you have all the quests, head for the mine.
It's best to complete all these quests at once. First - to warm up - hunt some Highland Cubs and gather their pelts. You need 6 of them. The same thing goes with Cave-Claws. You can find them in eastern part of Thorin's Gate, as well as inside the mine. Go to (3) and talk to Elladan. He tells you to go down into the mine.
Your goal is to search 4 goblin bodies that are laying here - you'll pick up their axes automatically. Go along the main corridors. Activate a pile of Rubble that you see at the end (*) - you'll find a scroll that Gailthin wanted. When both quests are marked by a tick on your list (in lower-right part of the screen), you can leave. Talk to Elladan once more. He tell you to take these axes to Dwalin, who can be found at Frerin's Court (4). Before you head there, go back to elf encampment and talk to Gailthin, Orodlin and Laergil to finalize their quests and get the rewards. When you have a choice in rewards, choose parts of equipment that your character can wear. Also, remember to equip all new stuff - by entering the inventory and double-clicking the appropriate item.
Dwalin can be found near Frenir's Court (4). He tells you to defeat one Goblin Prowler and search its corpse. Goblins can be found up the mountain in the North-Eastern part of Thorin's Gate, around Axe-Head Path (7). Loot the body and go back to Dwalin.
HINT: As soon as your character hits level 4, you should seek out your trainer and buy some new abilities.
Now is a good moment to get some more side-quests. There are two of them to get at Frenir's Court. Talk to Mathi Stouthand and Bogi (they're both near Dwalin). Their quests are related to each other and therefore best done at the same time. Bogi wants you to get 6 pieces of Auroch meat. These animals can be found in Eastern part of the area (4). You'll get new shoes for this one. Mathi wants you to get rid of an overgrown Auroch called the Frostmantle (4). In order to kill it without any problems, you probably should join forces with other players. Your reward for this quest will be the best weapon you can get in this chapter, so be sure to choose the one that suits you best and equip it.
HINT: If your character is not too strong in combat, you might have a little problem dealing with it. It's good to join forces with other players on this one. You don't have to enter any fellowships for now, but just help somebody who is fighting the auroch, then ask him politely to do the same for you when it respawns in a couple of seconds. Remember that the experience and loot for killing a monster goes to the player who first attacked it.
When you are done with all previous quests, Dwalin will order you to go to Goblin Cave and meet Elrohir in there. Before you go, talk to Erynwen (6) to get another side-quest from her - A Deadly Bloom. Go along the Axe-Head Path (2). When you reach the Goblin encampment, you'll see plants called Skorgrim's Bloom growing all over the place. Erynwen asked you to destroy 6 of these - you can do that by approaching each of them and right-clicking it. Be sure that there are no enemies around, as the action will be interrupted if you get attacked when performing it. You can now go further up the mountain, or go back to Erynwen and get your reward - a bow, a staff, and a shield - choose the one that's most useful to you.
The Goblin Cave is up the Axe-Head Path. Elrohir can be found at (*). The cave is filled with goblins, obviously, so watch out. Talk to the elf and you'll get a letter from him. Take it back to Dwalin to finish this quest. When you are ready, proceed with Dwalin's next request, which triggers the next instance.