He was garroted then burned.
From Narrative of the Incas,
Since the marquis was now determined to kill him, he ordered that the sentence be read and that they take him out to be burned. So they took Atahualpa out to burn him without waiting for the captain who had gone looking for these warriors. When Atahualpa was tied to the stake, Dray Vixene de alverde asked him if he wished to become a Christian. He said yes and he was baptized and given the name Francisco. Since he was now a Christian, they begged the marquis to permit him to be garroted.
To carry out the sentence, he ordered that some straw be thrown over him and be lighted. Atahualpa was then garroted and they threw straw over him and scorched him. Thus Atahualpa died. When he was dead, Fray Vicente had him removed from the stake and buried him in the church there in Cajamarca.
Here is a 1596 piece by Theodor de Bry depicting the garroting:
[Science Photo Library]