For the purposes of this walkthrough, we will start from the entrance from Darkroot Garden and down towards the open area. There is a Bonfire here guarded by a Black Knight if you keep going down from where you enter, which is also the path from the Valley of Drakes, then, head to the central area which connects Darkroot Basin to Undead Burg.
Immediately getting to the central area, you will become aggroed by a number of different enemies, namely the Crystal Golems ahead of you, but, as you attack them, you may find yourself getting hit by some ranged attacks. Try to deal with these relatively Weak Crystal Golems, and avoid the ranged blasts. After they're all dealt with, head to the front of the Basin to encounter a Hydra.
If you're looking for more help, our Dark Souls walkthrough and guide can help with all other areas of the game, including the dreadedTaurus Demon, Capra Demon, Ornstein and Smough bosses. Meanwhile, we have explainers on how to access DLC Artorias of the Abyss, the best gift and best class in Dark Souls, Dark Souls' best weapons, Dark Souls Covenants, Dark Souls Estus Flasks locations, Dark Souls Titanite Slab locations and NPC quests including Lautrec of Carim.
The Hydra is pretty mean, with the power of its ranged attack being dependent on how many heads it has left. But the Hydra has another attack as you approach it- it dips its head into the ground, this is your window to cut off the Hydra's heads. It should be a pretty simple pattern, just guard when it comes for you and you should have no trouble with slicing all of its heads off and getting a Dusk Crown Ring and Dragon Scale as a reward.
It's round here you can start to uncover the way to the Artorias of the Abyss DLC. Be careful with the terrain here, as the path in the water can suddenly drop, watch your feet for the path ahead. When the Hydra is dead, you will see a save up and to the left past the waterfall, make a mental note of this and head towards the waterfall.
To the right of the waterfall will be a very long ladder. Head up. Once at the top cross the bridge and hug the left to get a Soul of Brave Warrior, then head back and go up the ladder that you just passed, where you will find yourself back in Darkroot Garden.