Written by Andreas Ryu
Ulfric Stormcloak was chosen by the Greybeards to study the Way of the Voice which he did for 10 years and was trained to be a Greybeard but in 4E 171, when the Great War began he decided to leave High Hrothgar to join the Imperial Legion even though Arngeir the Greybeard who taught him the Voice thought he should use it to worship Kyraneth and not use it as a weapon.
Ulfric was a veteran of the Great War and fought against the Aldmeri Dominion along with Legate Rikke and Galmar Stone-Fist. during the war, he was captured by the Dominion and used him to try and take over the Imperial City but fortunately, he managed to escape before they were able to get any information.
4E 176 After the Legion signed the White-Gold-Cordonat which banned the Worship of Talos among other things Ulfric Stormcloak was enraged and it got worse when a group of Bretons called the Reachmen who are now known as the Forsworn took over Markarth but Hrolfdir Jarl of Markarth made a deal with Ulfric that if he retook the reach, than he would allow worship of Talos. Ulfric agreed and his militia took over the Reach. Madanach who was the leader of the reachmen was captured and was placed in the Cidhna Mine and Jarl Hrolfdir lived up to his promise and restored worship of Talos in Markarth for a while, when the Imperial Legion arrived, Ulfric refused to let them into the city until they agreed with free worship of Talos but deaths were keep rising and rising so the Legion had no choice but to restore worship despite it going against the White-Gold-Cordonat, The Imperial Legion hoped the Dominion didn't find out but eventually they did the Legion kicked out Ulfric and his army and arrested them with help of Jarl Hrolfdir. Some say this betrayal led to the Stormcloak rebellion.
Ulfric's father Hoag who was Jarl of Windhelm at the time, died while Ulfric was imprisoned, Ulfric eventually got out of prison and took the throne as Jarl of Windhelm.
4E 201 Ulfric Stormcloak challenged High King Torygg so he could show everyone that Skyrim was weak Torygg accepted the challenge and ends up getting killed by Ulfric. Many people saw the duel as murder.
4E 201 17th of Last Seed Ulfric, some Stormcloak soldiers, and a prisoner who was later found out to be the Dragonborn was ambushed by the Imperials in Darkwater Crossing and taken to Helgen to be executed. During the execution, a dragon who was later discovered to be Alduin the World Eater attacks Helgen destroying it. A few people managed to survive the attack including Ulfric and the Dragonborn. Weeks later after the attack on Helgen, the Dragonborn joined the Stormcloak Rebellion and was ordered to go to Korvanjund with a group of Stormcloaks to retrieve an artifact called the Jagged Crown. After retrieving the crown, Ulfric had the Dragonborn deliver his axe to Balgruuf the Greater, the Jarl of Whiterun if he keeps it, he will be allies with the Rebellion if he returns it, it will be an act of war. Balgruuf returns the axe to Ulfric days later, The Stormcloaks attack Whiterun and end up taking it over. Balgruuf the Greater gets kicked out and Vignar Gray-Mane takes place as Jarl of Whiterun. With the help of the Dragonborn, Ulfric takes over almost every Imperial controlled city, Ulfric plans an assault on Solitude where many Imperials and Stormcloaks die but Ulfric, Galmar Stone-Fist, and Dragonborn infiltrate Castle Dour where Legate Rikke, an old friend of Ulfric and General Tullius is. Rikke and Tullius fights back but Rikke ends up dying and Tullius is taking his last breaths Ulfric decides to give the Dragonborn the honor to kill Tullius. After the war was over, Skyrim convened a Moot to elect a new High King and Ulfric becomes the High King of Skyrim.
I wrote this fan biography of Jarl Ulfric Stormcloak to be like the books in the Elder Scrolls and if there was any details I got wrong, please let me know.