Dragon Slayer Ornstein and Executioner Smough

Dragon Slayer Ornstein and Executioner Smough are a pair of bosses that guard Gwynevere, Princess of Sunlight in Anor Londo.

Alongside Hawkeye Gough, Artorias the Abysswalker and Lord's Blade Ciaran (all of whom appear in the Artorias of the Abyss DLC), Dragonslayer Ornstein was one of Gwyn's four knights.

Summoning
It's possible to summon Solaire of Astora to help in the fight. His summon sign can be found on top of a small platform connected to the stairs to the left, when facing the fog door (the platform below the archer knight).

If he starts the encounter at full health, Solaire can generally solo one of the bosses, as long as he's not attacked by the other (i.e., if the player keeps the other boss busy). Note that this can make it harder to ensure a specific kill order (necessary to determine the final loot, as described below), as there is no way for the player to tell Solaire to stop attacking a specific boss.

Strategies
The player must fight both at the same time. When one is killed, the other absorbs some of his power, receiving an HP, damage, and resistance boost, and healing back to 100%. He will also take on a physical characteristic of his fallen comrade: Ornstein grows in size while Smough is imbued with lightning.

Having a summoned phantom can make the fight significantly easier, as it allows the bosses to be fought separately. Note, however, that there's no advantage in damaging both bosses during the first phase (as mentioned above, the surviving boss' HP goes back to 100% when the second phase begins). The role of the second player is simply to keep one of the bosses busy while the other is killed.

When fighting alone, one of the safest strategies is to kite the bosses around the outside of the room, keeping both in view and using the pillars to block their charging attacks. This will generally result in Ornstein dying first, since he moves faster and will usually catch up to the player while Smough is still trying to get around the previous pillar.

Killing Ornstein first is generally regarded as making the encounter easier to win, since Smough has more weaknesses and is more predictable than his partner in the second phase.

For melee characters, using a weapon with good reach (such as a spear, halberd or a sword with a fast thrusting attack) will make it significantly easier to hit the bosses when they are near a pillar. Note that both bosses can hit through the pillars with some of their attacks.

Ranged characters using the pillars to control the movement of the bosses should note that not all pillars are the same height; some will block projectiles while others will not.

When Smough uses his charge attack players need to make sure that if they dodge, they dodge just before he swings his hammer upwards because if the player dodges too early, Smough will still reach them. Make sure that Smough is just beginning his upwards swing then dodge, if done correctly he should miss. This is easier if light armour or medium armour with Havel's Ring are equipped.

Swinging Combo
Ornstein swings his spear up to four times in a row. This attack can be blocked, and generally offers a good chance to counter-attack.

Jumping Attack
Ornstein jumps up, and then either stabs at the player, or smashes his spear into the ground where the player is standing. Both deal the same amount of damage, and can be blocked.

Charging Spear
Ornstein glides towards the player, and then stabs with his spear. The attack can be blocked or dodged, and a counterattack is possible to achieve. Note that this attack can (rarely) cause Ornstein to move through a pillar.

Lightning Spear Charge
Rare attack that is identical to Charging Spear, except Ornstein imbues his spear with lightning before charging.

Lightning Banzai Drop
Only used if Smough was killed first. Ornstein jumps up, pauses mid-air, then falls onto the ground, causing a wide lightning field created from the point of impact. This cannot be fully blocked, and can only be dodged by keeping one's distance. Smough's distinct laughter can be heard during this attack.

Quick Lightning Spear
Ornstein uses his weapon's power to shoot a small burst of lightning at the player. This attack is rarely used.

Heavy Lightning Spear
Ornstein charges up a lightning bolt that he fires at the player. This Lightning Bolt is unusually slow once fired and has strong homing capabilities.

Lightning Impale
In Ornstein's large form, he will charge his spear with lightning, and then lunge at the player in a quick stabbing motion. If this attack hits a player who is not blocking, Ornstein will raise the player and release the charged lightning, dealing huge amounts of damage.

Joust
Smough charges at the player with his hammer, then swings it upwards diagonally when he reaches the player. This deals heavy damage, especially when in lightning form. It can be avoided by running directly away or with the right dodging speed. Blocking will break the player's guard if they are using a shield of inadequate stability. While pillars will block Smough's movement, the hammer itself will go through the pillar.

Swing
Smough swings his weapon. It is possible to roll under this attack and start attacking before Smough has time to recover. Blocking this attack may use a large amount of stamina. May follow up with a second swing.

Smash
Smough slowly raises his weapon and then hammers the ground in front of him. This attack can go through pillars. May follow up with a swing.

Jumping Hammer
Smough jumps into the air and then hammers the ground as close to the player as he can get. This can be avoided by rolling in any direction while Smough is airborne.

Banzai Drop
Smough jumps into the air and then crashes into the ground below. Smough takes a while to recover after using this attack. When in his more powerful form, there is a lightning area of effect upon landing. The only way to fully avoid the lightning damage is to be out of its range (dodging while inside the range will not give immunity). It can also be partially blocked with a shield.

Trivia

 * If Ornstein is defeated first, his hand appears to move just before being hit by Smough's hammer, suggesting he was still alive and that it was Smough who gave the final blow, living up to his title as executioner. If Smough is defeated first, Ornstein respectfully places his hand over his body to absorb his power.
 * In co-op it is possible for multiple players to be caught by Giant Ornstein's Lightning Impale attack at the same time. However when this happens, interestingly neither player will take any damage from it.