Meet with Legate Rikke
Defend the Barricades
Take a position depending on your play-style. Ranged fighters will want to either be on the other side of the barricade, if they can get very quick kills consistently, or on the wall if they are more lightly armored. For brawlers and more heavily armored fighters, get on the other side of the barricade and then take the fight to them.
To complete this you will need to then fight off a set number of Stormcloak Soldiers. There will be a few generals in the mix as well. Expect this to a long fight. Have plenty of potions on hand to help with that.
Report to the Jarl of Whiterun
With the assaulting forces defeated, make your way back to Dragonsreach. Talk with the Jarl to finish this quest.