Here's Jaime's account of the events, from the books.

“My Sworn Brothers were all away, you see, but Aerys liked to keep me close. I was my father’s son, so he did not trust me. He wanted me where Varys could watch me, day and night. So I heard it all.” He remembered how Rossart’s eyes would shine when he unrolled his maps to show where the substance must be placed. Garigus and Belis were the same. “Rhaegar met Robert on the Trident, and you know what happened there. When the word reached court, Aerys packed the queen off to Dragonstone with Prince Viserys. Princess Elia would have gone as well, but he forbade it. Somehow he had gotten it in his head that Prince Lewyn must have betrayed Rhaegar on the Trident, but he thought he could keep Dorne loyal so long as he kept Elia and Aegon by his side. The traitors want my city, I heard him tell Rossart, but I’ll give them naught but ashes. Let Robert be king over charred bones and cooked meat. The Targaryens never bury their dead, they burn them. Aerys meant to have the greatest funeral pyre of them all. Though if truth be told, I do not believe he truly expected to die. Like Aerion Brightfire before him, Aerys thought the fire would transform him . . . that he would rise again, reborn as a dragon, and turn all his enemies to ash.

“Ned Stark was racing south with Robert’s van, but my father’s forces reached the city first. Pycelle convinced the king that his Warden of the West had come to defend him, so he opened the gates. The one time he should have heeded Varys, and he ignored him. My father had held back from the war, brooding on all the wrongs Aerys had done him and determined that House Lannister should be on the winning side. The Trident decided him.

“It fell to me to hold the Red Keep, but I knew we were lost. I sent to Aerys asking his leave to make terms. My man came back with a royal command. ‘Bring me your father’s head, if you are no traitor.’ Aerys would have no yielding. Lord Rossart was with him, my messenger said. I knew what that meant.

“When I came on Rossart, he was dressed as a common man-at-arms, hurrying to a postern gate. I slew him first. Then I slew Aerys, before he could find someone else to carry his message to the pyromancers. Days later, I hunted down the others and slew them as well. Belis offered me gold, and Garigus wept for mercy. Well, a sword’s more merciful than fire, but I don’t think Garigus much appreciated the kindness I showed him.”

^{A Storm of Swords, Jaime V}

But when he closed his eyes, it was Aerys Targaryen he saw, pacing alone in his throne room, picking at his scabbed and bleeding hands. The fool was always cutting himself on the blades and barbs of the Iron Throne. Jaime had slipped in through the king’s door, clad in his golden armor, sword in hand. The golden armor, not the white, but no one ever remembers that. Would that I had taken off that damned cloak as well.

When Aerys saw the blood on his blade, he demanded to know if it was Lord Tywin’s. “I want him dead, the traitor. I want his head, you’ll bring me his head, or you’ll burn with all the rest. All the traitors. Rossart says they are inside the walls! He’s gone to make them a warm welcome. Whose blood? Whose?”

“Rossart’s,” answered Jaime.

Those purple eyes grew huge then, and the royal mouth drooped open in shock. He lost control of his bowels, turned, and ran for the Iron Throne. Beneath the empty eyes of the skulls on the walls, Jaime hauled the last dragonking bodily off the steps, squealing like a pig and smelling like a privy. A single slash across his throat was all it took to end it. So easy, he remembered thinking. A king should die harder than this. Rossart at least had tried to make a fight of it, though if truth be told he fought like an alchemist. Queer that they never ask who killed Rossart . . . but of course, he was no one, lowborn, Hand for a fortnight, just another mad fancy of the Mad King.

^{A Storm of Swords, Jaime II}