Hercules was killed by burning himself alive on a funeral pyre after being poisoned by the blood of Nessus.
Here's a more detailed explanation:
Hercules' death came about through a tragic chain of events involving his wife, Deianeira, and the centaur Nessus:
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The Centaur's Deception: While crossing a river, Deianeira was assaulted by the centaur Nessus. Hercules shot Nessus with a poisoned arrow (the poison being from the Hydra). As he was dying, Nessus tricked Deianeira, telling her to collect some of his blood, claiming it would act as a love potion to ensure Hercules would always remain faithful to her.
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The Tunic of Poison: Years later, Deianeira, fearing she was losing Hercules' love to another woman, soaked a tunic with the "love potion" (Nessus's poisoned blood) and gave it to Hercules to wear.
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Agony and Death: As soon as Hercules put on the tunic, the poisoned blood began to burn his flesh intensely. The pain was unbearable.
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The Funeral Pyre: Realizing there was no escape from the excruciating agony, Hercules, to end his suffering, built his own funeral pyre on Mount Oeta and had himself burned to death.
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Ascension to Olympus: After his death, Hercules's mortal remains were consumed by the flames, and his divine spirit ascended to Mount Olympus. Athena then brought him to Olympus on her chariot, where he became a god.
