Detail of Heracles bow, which he hung of during the fight with the Nemean lion. From a Roman sarcophagus. Notice that the bow, hanging in a tree, is a common way to recognize the hero.
Exactly what tasks Heracles had to endure under Erystheus is uncertain - the earliest sources don’t even mention the so called labors, they only hint that he did great deeds. I, however, would like to present the 12 labors, which are mentioned in “later” works, in the traditional order.
The first labor was the fight with the Nemean lion. This was a great beast lurking in an area close to Mykene (called Nemea) and the hero was instructed to kill it. On his way to the lion’s den Heracles found an old man who was about to sacrificing to Zeus Sotor (an aspect of Zeus, the king of the gods) and he told the man to wait 30 days so that they could celebrate the sacrifice together. If he, Heracles, on the other hand was killed in the fight, he asked the old man to sacrifice to him as a hero.
Heracles then went on to fight the lion and found it in its den. The hero attacked it with his bow, but the skin deflected the arrows. He then tried to kill it with his club, which could not hurt the animal. At last he blocked one of the entrances to the den, went in himself and strangled the animal and then peeled of the skin with its own claws. This is one of the stories about how he gained his lions skin.
He then proceeded by returning to the old man who had given up hope (and was about to sacrifice on his own) and they sacrificed together. It is said that Erystheus was so scared when Heracles returned with the skin after this first labor that he tried to hide from him.