Cemetery of Ash
Ashen Estus Flask
This is where you start the game, having awoken from a stone coffin.
You awake in the Cemetery of Ash near to your recently upturned coffin. Follow the path forward and read the messages on the ground if you don't know the controls. Defeat any enemies that attack you, they can drop Fading Souls.
As you continue forward you will eventually come across a broken fountain with a corpse lying beside it. Take the Ashen Estus Flask and continue forward out of the flooded ruins and rest at the bonfire overlooking the mountains.
From the bonfire, head down the path into the ruined courtyard where you will find a immoble Iudex Gundyr. Walk up to him and examine the Coiled Sword to pull it out of him. This will start the Iudex Gundyr boss fight.
To Firelink Shrine
Having defeated Iudex Gundyr, rest at his bonfire, then continue out of the courtyard. Pick up the Broken Straight Sword next to the gravestone to the left, then continue right. Watch out for the Hollows.