Battle for Whiterun (Stormcloaks)

Break Through The Enemy Barricade
The walls of Whiterun are defended by both Whiterun Guards and Imperial Soldiers. The barricade is a simple wooden one that is easily destroyed in a few hits. As soon as it is destroyed, you can move on to your next objective.

Open The Drawbridge
Past the barricade you will encounter a few more soldiers. Fight through them then head up the battlements around the left side of the drawbridge. Directly above the bridge is the windlass used to lower it. Once the gate is lowered the defenders will retreat back into Whiterun, and the Stormcloaks will pursue them.

Force Jarl Balgruuf the Greater To Surrender
The battle rages on in the streets of Whiterun. Several of Whiterun's populace can be encountered on the streets but are non combatants and it is still considered a crime to attack them openly. You need to fight through the city to Dragonsreach. Upon entry, three guards will attack you, who can be killed in one shot by any attack. The Jarl himself will attack you with three guards and his Housecarl, Irileth. You don't have to kill any of the guards, as long as you can get Balgruuf on the ground and make him surrender.

Accept Jarl Balgruuf the Greater's Surrender
When Balgruuf surrenders, Vignar will walk in. After an argument over their views on the war, Balgruuf will face the player and say that he thought better of him/her. He will then go to gather his belongings, and Galmar will tell the Dragonborn to return to Windhelm with news of their victory.

The Differences Made To The City

 * The town guards are replaced with Stormcloak soldiers.
 * The new Jarl is Vignar Grey-Mane.
 * Olfina Gray-Mane becomes the new Housecarl to the new Jarl.
 * Brill becomes the new steward.
 * The Battle-Borns are harrassed and robbed, blaming it on the change in government.
 * Adriane Avenicci's dialogue will change.
 * The preacher of Talos, Heimskr, becomes a very happy man, even though he cannot enter his house, for it is sealed with debris and is missing most of the roof. Instead, he has a small tent next to the wall surrounding Jorrvaskr. This means a quest from the Thieves Guild from Vex cannot be completed.
 * The town has a few scars from the battle. The area around the Gildergreen tree is badly damaged.
 * Jarl Balgruuf, Commander Caius, Hrongar, Proventus Avenicci and Irileth take up residence in The Blue Palace in Solitude.
 * NOTE: If you follow the Jarl to his quarters after the fight, Galmar will become hostile when you kill the whiterun guards before they become hostile. It is unknown if this is a bug. So after you go in to Dragonsreach, wait for the Whiterun guards to become hostile before you kill them
 * Severio Pelagia's house is no longer accessible, due to debris blocking the door and damage to the roof. Heimskr's house is also inaccessible, for the same reason.
 * Fort Greymoor will be taken over by Stormcloaks with Horses to ride.

Bugs

 * Unless otherwise stated, the information above was obtained from in-game play or from The Elder Scrolls V: Skyrim Creation Kit.