Getting to the Dancer
The Dancer can be fought when you meet and kill Emma in the cathedral in the High Wall of Lothric. It's not recommended unless you are highly skilled as the Dancer is one of the more difficult bosses in the game.
The other intended way to defeat the first three Lords of Cinder (Abyss Watchers, Aldritch, Yhorm). When you do this, you will teleported to the High Wall cathedral, where you can start the fight.
The Fight
The Dancer has a weakness to Lightning, so bring weapons buffed with Lightning. All her attacks do high damage and require almost-perfect dodging. Don't bother trying to attack the Dancer from a distance as she will close in on you instantly. There are three attacks in particular to watch for:
Grab Only used in Phase One, the Dancer will perform a slow sweeping grab with her empty hand. Getting caught by this will almost certainly kill you so either roll backwards or towards the grab, as rolling sideways will get you caught.
AoE Explosion The Dancer will raise her hand and press it into the ground. This will cause a fiery explosion around her. While she is immobile during the attack, keep some distance unless you want to tank the explosion.
Fiery side attack She'll stick the sword into the ground and move it around in a semi circle, which will cause the line to explode. Move around her when she does this and hit her when she's done spinning. If you don't feel up to the risk, move away.
When she reaches 50% hp, she will gain access to another sword and proceed to spin horizontally multiple times before stopping and doing 2 more rapid spins. While it may seem counter-intuitive, attack her while she pulls the second sword out and stick to her rear as she spins around. You'll be completely safe and untouched, just remember to roll when she does the rapid spins. From here, it's just a matter of dodging her fast combos and finishing her off.
As a side note, you are able to summon the Sword Master for help if you have defeated him outside Firelink Shrine and have not killed the Vordt of the Boreal Valley. Because you need to kill Vordt to progress past High Wall, you will have to kill Emma to take this road which, again, I do not recommend.