When you begin the game, you will see a woman in a makeshift boat - this is Senua, the protagonist of the game. First, there's a lengthy introduction, where you will learn the outline of the plot and, for the first time, hear the voices haunting her.
After a few minutes you will reach the shore - go forward until you see a stone Lorestone. Interact with it and you will learn a chunk of the lore. These things are entirely optional, but they contain very interesting bits of story. It's worth investing some time to explore locations.
Keep moving forward, jump over the trunk and get into water. The darkness will soon start chasing you - run straight ahead until you reach a black tornado. The darkness will disappear, and you will see your destination - Helheim. On a beach, you will find another Lorestone - go left until you reach stone stairs, next to which another Lorestone will be standing.
Go up the stairs and then take the ladder. Follow the trail until you reach a narrow footbridge. You have to get onto the other side - be careful though, as you have to balance and maintain your equilibrium, or Senua will fall into the abyss.
Jump down on the other side and you will reach a gate with a weird symbol. Interact with it and you will be able to see the symbol. In order to be able to proceed, you will have to find the symbol on a wall of the cave. The solution can be seen above. When you manage to locate the shadow, the doors will be opened.
Go further, take the ladder and go through another narrow footbridge. On the other side you will see another Lorestone. Enter the cave, go down the ladder, jump down, take the narrow passage and you will reach a big courtyard with a gate. When you approach the gate, shadows will appear, and you will begin your first fight of the game.
Treat this fight as practice. In time, the enemies will be more numerous and stronger, so spend some time on practicing different moves. Defeat smaller enemies, and shadows will soon appear. Unfortunately, you cannot defeat these enemies - deal a couple blows, dodge their attacks, and a cut-scene shall commence soon.
From this moment on, every time the protagonist dies (either in combat or during action sequences), the black mark on her arm will grow. When it reaches her head, the game is over, and all your progress is lost. Don't worry however, because the game offers you a hand - the difficulty is constantly being balanced: if you die often during a particular fight, it will become easier. Besides, the higher the mark reaches, the slower it grows.
Approach the Lorestone to listen to more tales. Now you can choose a kingdom to go to - either The Lair of Valravn, the master of illusion and ravens or to The Land of Surt, a fire giant.