As the last quest available in Act I, Sisters to the Slaughter will require that you seek out and destroy Andariel, the Maiden of Anguish. Though your objective has likely been assumed while playing through Act I, it will be Deckard Cain who actually assigns this quest.
Andariel can be found on the final floor of the Catacombs. The entrance to the Catacombs is located inside the Cathedral, which is accessible from the Inner Cloister. Andariel is nearly always surrounded by groups of various monsters, so it is recommended that you dispatch them before doing battle with her. She has a powerful Poison attack, so having some Antidote Potions handy is a good idea. Items that grant Poison Resistance or reduced Poison duration are also useful against Andariel.
Defeating Andariel will grant you access to Act II and the deserts of Lut Gholein.
Tactics Defeating Andariel
In case your having trouble defeating Andariel you can go to the menu and select Save & Exit. Your character is saved completely, and all monsters are respawned, so you can go back and fight them again for more experience in order to level up. Remember, Andariel has a weakness for any fire based damage, so try to use your fire skills as much as possible. Amazons can use Fire Arrow, Paladins can use Holy Fire, Sorceresses can use any fire skill she might possess, and so on. Barbarians can augment their weapons with rubies or use charms to increase their fire damage.
Here are some helpful hints on how to beat her with different classes:
Amazon - If you have a bow, it's a good idea to use it. Using a bow from long range allows you to stay away from Andariel and possibly dodging some of her Poison attacks. Any skill like Fire Arrow or Cold Arrow helps kill her easily by doing extra damage.
Barbarian - To kill Andariel slightly easier, use your best damaging weapon. If you use dual weapons, then using skills like Double Swing are excellent. If your weapon has Mana Stealing/Life Stealing and is able to dual wielded, using Double Swing makes you able to do more damage by getting mana back to use Double Swing more, or by stealing Andariel's health.
Druid - If you're a Druid, use Molten Boulder or your best ranged weapon or spell. It is a must to stay away from Andariel's Poison attack in anyway possible. It can be very deadly, unless you have tons of hit points. If you are a Shape Shifter, Werewolf can be good for fast damage, or Werebear for added hit points and damage.
Sorceress - The Sorceress is an excellent spell caster. The main downfall for the Sorceress is her weak armor and health but, if you can get Andariel into the room outside her starting room, and get her stuck on one side of the lake, bombard her with as many spells as possible before she can attack you. If she comes at you from the other side, use one of your Cold Spells to slow her down. Static Field is quite effective here. Use it once or twice to drop Andariel's hit points by about 1/3 or so to give you an edge.
Necromancer - If you use summoning skills, make sure to kill the creatures in Andariel's throne room before the fight. These corpses will provide a nearby place to raise more skeletons. Also, keep a golem (If you have one) in action at all times, as they are good tanks for the weaker skeletons.
Quest Activation Dialog
Deckard Cain:"It is certain that we face the demon queen, Andariel, who has corrupted the Rogue Sisterhood and defiled their ancestral Monastery. This does not bode well for us, my friend. Ancient Horadric texts record that Andariel and the other Lesser Evils once overthrew the three Prime Evils - Diablo, Mephisto and Baal - banishing them from Hell to our world. Here, they caused mankind untold anguish and suffering before they were finally bound within the Soulstones. Andariel's presence here could mean that the forces of Hell are once again aligned behind Diablo and his Brothers. If this is true, then I fear for us all. You must kill her before the Monastery becomes a permanent outpost of Hell and the way east lost forever."
NPC Quest Dialog
Akara:"Andariel has desecrated all we hold dear. She must not be permitted to serve Diablo. Destroy her! Her corruption of our Order must be undone!"
Charsi:"Send Andariel back to the Hell she came from!"
Deckard Cain:"Diablo is heading east for some foul purpose. And the only passage east is through the Monastery gate. Obviously, Diablo summoned Andariel to block any pursuit. For her part Andariel hopes to win Diablo's favor... the lesser demons are always vying for positions of power within the unholy hierarchy!"
Gheed:"You're going after Andariel? ...One of my wagon wheels is in need of repair. I'll be under the wagon, if I'm needed."
Kashya:"I can imagine a thousand different ways to kill Andariel. You need only choose one."
Warriv:"The mapmakers tell us the shortest distance between two points is a straight line. Our way east is a line that runs through Andariel's stronghold, the Monastery."
Akara:"You have done much to help us, but I sense that this has only fueled Andariel's fury. She will not stop until we are all dead. You must kill Andariel before her army can gain the upper hand."
Charsi:"If you are the hero that you seem to be, now is the time to prove it."
Deckard Cain:"It is clear that Andariel is acting on behalf of Diablo to prevent anyone from following him eastward. Her defeat would allow you to continue the pursuit. Ancient lore has it that while Andariel was spawned in the Burning Hells, she is not fond of fire."
Gheed:"Have you stumbled upon that Demon Queen, yet? I hear she's quite the beauty... as far as Maidens of Anguish go, that is."
Kashya:"Deckard Cain has important information about Andariel."
Warriv:"May I remind you that my caravan can only go east if the Monastery is cleansed?"
Akara:"Finally, we may rejoice! We owe you a debt we can never repay. I only hope that in time we will be able to rebuild our Order. All our thanks go with you, my friend."
Charsi:"You'll probably go east now... It was good to know you. I hope you'll come back if you ever need anything."
Deckard Cain:"This is a great victory indeed, but many more battles await. I will accompany you on your journey, lending what assistance I can... Remember... Diablo is still out there, seeking something in the desert. I'm afraid that this nightmare will not end until you find what it is that he seeks."
Gheed:"I'm going to party like it's 999!"
Kashya:"Andariel's death brings about renewed life for us all. We mourn the loss of our dear Sisters, but at least now we can get on with our lives. I... may have misjudged you, outlander. You are a true hero and testament to the noble spirit which has inspired our Order for generations. Fare well... my friend."
Warriv:"The caravan is prepared. We may now journey eastward to Lut Gholein."
Character Quest Dialog
Amazon:"This maiden shall inflict no more anguish."
Assassin:"Death becomes you, Andariel."
Barbarian:"Let the gate be opened."
Druid:"Andariel, your reign is over."
Necromancer:"Back to the Hell that spawned you, Andariel."
Paladin:"My work here is finished."
Sorceress:"The evil Queen has fallen."