Lots of people disregard the story for being shallow, but in reality, if you dig deep enough you will eventually realize that the world is filled with background and history. There isn't much Story to Dark Souls in the traditional sense, as most of the game’s lore is hidden in conversations you have with various NPCs as well your own interpretations of what’s happening in the world. There isn't a strictly guided structure as to how you should approach the game, but there are certain events that needed to be completed in order to further progress the story.
You can climb up towards Undead Burg or venture below to New Londo Ruins.
As soon as you finish the introductory part of the game, you will be thrown into this massive world and left to explore it as you see fit. Unlike Demon’s Souls’ structured hub approach, Dark Souls is set in a huge open-world.