This side quest can be started when the party meets Degrodel in his house, in the northwestern area of Baldur's Gate. The mage Degrodel has information on where the Helm of Balduran may be found and if the party can find the item and bring it to him, he will give the party a large sum of 5000 gold. Degrodel's house is guarded by six hostile creatures; specifically, two Doom Guards, a Helmed Horror, and three Invisible Stalkers.
The information Degrodel has is that the item is in the possession of someone who tried to break in Razamith's Tower and he and his companions were turned into stone by the mage Razamith. The statues are now in someone's atelier in the market district. He will give you six scrolls of Stone to Flesh. Your task is it to break in the atelier and cure their petrification and take the helmet from them. The manner in which it is done doesn't matter to the mage, as long as you return with the helmet.
When you cure Vail, the leader of the party from petrification, he asks why you have cured him. From this point you can either try to kill him and his party as he doesn't want to give his helmet voluntary or you can let him go. If you let him go, he will grant you ownership of the Cloak of Balduran, which now in the possession of Quenash, a prostitute who lives in the Undercellar.
Quanesh questions your acquaintance with Vail and you must answer her question correctly. If you do so, she will give up the cloak and you can question her where the Helmet of Balduran is. She will say that Vail has hidden the helmet in some inn with the name of the items.
You can find the helmet behind a trapped painting on the back wall of the second floor of that inn. After you have found it, you can either sell the helm and complete the quest or keep it for yourself. Also you can give the helmet to Degrodel and then kill him, with no reputation loss, to get the helmet back. This latter option is satisfying as, even if you give him the Helm, he'll summon some Doom Guards and Helmed Horrors, and then cast Shadow Door to leave. A good way to kill him is using the Haste spell, Arrows of Detonation and the Fireball spell, which also damages the Doom Guard, Invisible Stalkers and Helmed Horror.