You begin the game atop the hill within the walls of Brighthelm, the last viking settlement free of Hel's reign on the island of Niflberg. Skarin stands within a portal of sorts, surrounded by glowing stones. This is the Brighthelm leystone - you will appear here upon dying. On your minimap you'll notice green dots as you move around - these are significant NPC's, such as shopkeepers and quest givers.
Make your way to the right, and speak to the oracle girl who will tell of the dragons. Head down the hill (either jump or run down the path), and make your way to the commander at the beach head. He'll open the gates for you. Speak to Torv the Innkeeper on the east side of Brighthelm, and you'll receive the task of finding mead. Mead is one of the best ways of acquiring gold, so keep a look out for barrels shining white.
If you want some quick cash, head down to the beach and look for the bags of cash, the barrel of mead, and the two groups of vikings tied to poles. These captives can be freed to aid you in battle later on, so if you want a more successful and large scale battle, look for your allies all the time.
When you're ready to move on, head east out of Brighthelm and follow the path.
The Ruins
Following the path east, you'll see it fork around a mountain, with a bridge to the right. Head underneath the bridge and break the urn, then run back up the hill and onto the bridge, jump across the gap, and continue to kill the undead vikings who are feeding on dead bodies. There will be one straight and on the right, one straight forward, and then as you follow the path to the left there will be two more at the intersection with the trail up ahead (when it curves right, they'll be feasting like the other two). Additionally, if you go back to the area between these 2 pairs of grunts, there's a cave located in the large rock on the left side (the north). You can climb the small steps into the cave and slay the enemies there to retrieve some gold.
If you like, you can take this time to check out the arena, because it's isolated on the beach. Choosing to head down there now, you'll find one urn near the cliff wall below where the two Legion Grunts were feasting. Additionally you'll find a barrel of Niflberg Mead located near the arena, along the cliff wall. Don't fall into the water, as you'll take damage rapidly, but go up into the arena circle and stand in the middle. Interact with the platform and a warrior from Valhalla will greet you, and a shop menu will appear. If you have enough money, you can get more than simply the free ability that's available.
When you're ready, head up the trail where you left it, and run up the path to where it opens (in the direction of the leystone). If you look down the path you'll notice a large group of grunts located around a center area, and a wooden cage-like structure in the back. That structure has some ally vikings in it, who are willing to help fight with you. Grab the leystone, then sneak around the left side and to the back where you can free your allies to help you take on the other grunts located around the center area. If you happen to grab the attention of all of them, either fight to the death (not recommended, as you won't have the fighting techniques unlocked to give you an advantage) or run until they retreat. Do not jump off the cliff down to the beach unless you have full health, for the drop will reduce your life significantly, depending on the location you fall from.
Again, you have options in this situation: you can sneak around and try and pick off the enemies, you can take them all on at once, or you can attempt to recruit help to fight for you. Upon defeating all the enemies, Hel's influence will be purged from the area and the weather will become bright and sunny. Open the cage if you haven't done so already, and wait for the men to spread out. One will be standing next to the cage entrance, and a green dot will appear on your minimap. Talk to this man, who will tell you about a traitorous viking who fled when their forces were captured. Your missions is to slay this man, and bring back his helmet.
The Traitor
Use Brisingamen to look at your map. You'll see a circled "X" marked on your map just north of the arena. Scroll to it and press 
/
- this will make a white arrow appear on your minimap, which you can follow to your next objective (the location of the traitor).
Following the path back down the ruins, to where you can access the beach safely, you'll notice a beached longboat up ahead. Run over to it, and you'll be greeted by Legion Grunts, and eventually a cutscene when you get close enough to the traitor. He'll tell you why he left his men for Hel, and gladly fight you to the death. Take out the closest grunts, and then run to the back of the camp and up the wooden ramp to slay the two Legion Archers (these are very annoying when fighting other enemies). Finally, take on the traitor - the best technique is to block and then shoulder shove him over and use the time he's on the ground to attack. Sometimes this won't work (he guards a lot), but every once in a while the game will allow you to strike him.
After receiving the traitor's helm, collect all the gold back and head back to the ruins to talk to the guy by the cage. He'll tell you his men have joined your cause - the helm will be removed from your inventory, and a small notice in the bottom left will appear, saying "Army has Increased." Although this is true, you won't see additions in Brighthelm.
Before leaving the ruins, there is some treasure to be gotten. First of all, there are several urns and gold bags, and two treasure chests. One of the chests contains the Hugin gem, which is a major requirement for defeating Hel's forces on Niflberg. To get the Hugin gem, head to the leystone, and head around the ruins on that side. The first ruin corner you come to will have a stairway you can run up. If you go down, you'll find two bags of gold. Head up the stairs, then climb the bushes on the wall (just walk up to it). When you get to the next large flat area, climb over to the edge and touch the ground to dismount off the wall. Open the chest, then continue exploring the area if you wish. If you don't want to waste time, come back here after you've acquired the three maps for locating treasure, otherwise if you want to save money (there's no reason because if you acquire it all you'll have excess).
You have three choices now: you can walk down to the arena and unlock a new ability (your best bet is to unlock one of the rage moves, because you'll have access to powerful combo attacks that are also useful in destroying shielded foes), return to Brighthelm via the leystone and purchase a rune if you haven't done so already (ice or fire is the most useful) as well as return the Niflberg Mead, or head to your next objective. Since the game is somewhat open, you're free to explore anytime. When you're ready, head up into the hills to take on the forces stationed at Hilltop Farm.