You can approach the forest from two different sides
Past the bridge, there are two paths going into the forest. On the right, you will be attacked by lizard-like monsters. Follow the path that they came in here through. The location is very similar to Darkroot Garden. You will encounter a lot of lizards and giants here.
You need to watch out for their attacks with the hammer. The best tactic is to dodge from its attacks and strike from behind. They drop Twinkling Titanite.
As you walk along the right forest wall, you will reach ruins. Watch out for the hole on the left. Once you climb up the stairs, you will find an item.
Around the meadow on the right, you will find an item. Then, cross another bridge.
Once you approach it, there will appear a black dragon. However, just like in the case of the Undead Burg, it will fly away in a moment. Past the bridge, turn right and walk along the wall.
After you have gone past the narrow passage, climb lower. Keep going ahead, at the slope, you will find an item. Here, there also is a big group of enemies. It is best to lure them out, one by one, and eliminate them successively.
On the right, there is another building. Inside, activate the elevator and go down.
On the right, there is a soul. There are three paths coming from here. First, cross the bridge and talk to the man at the end. Respond positively to his question. From now on, you are able to buy items from him.
As you proceed, you will reach an elevator. Unlock it and you will unlock a shortcut to the previous location.
Then, walk through the mist. This will start a battle with Artorias Knight.
After the fight with Artorias, in the middle of the arena, you will notice a kneeling woman. Tal to her. You can give her the Soul Of Artorias, in exchange for which, you will receive Dark Silver Tracer and Gold Tracer.
At the exit from the arena, there are two paths. If you go right, you will reach the PvP arena, to the left, the tower spire. You will return here later. As for now, go straight ahead.