There are different stories on this; he either strangled it, or shot it with a specially created arrow.
Hercules killed the Nemean lion as part of his Twelve Labors assigned to him by King Eurystheus. The Nemean lion was a fierce monster terrorizing the region of Nemea, and Hercules was tasked with slaying it as his first labor.
Fittingly in Nemea. (Peloponnesos, Greece)
He wore the skin of the Nemean Lion after he had to kill and skin it during the 12 Labours of Hercules.
During the 12 Labours of Hercules, he killed The Nemean Lion, The Lernean Hydra and The Stymphalian Birds
The Nemean lion.
King Eurystheus decided that Hercules had to kill the Nemean lion, that tormented the citizens of his country. Hercules was to bring him the lion's skin within a month. When he returned, the King let him keep the skin of the Nemean lion. Hercules wore it to show his courage and strength at killing one of the strongest lions that existed.
Hercules had to slay the Nemean lion.
The Nemean Lion was the only lion to have a special type of fur.
The Nemean lion.
The Nemean Lion was slain by Hercules as the first of his Twelve Labors. The lion's hide was impervious to weapons, so Hercules strangled it with his bare hands and used its own claws to skin it.
Hercules/Heracles killed the Nemean Lion and the Hydra.
The city of Nemea - hence the Nemean Lion.