We pick up this third part of the Labours series with the second labour Hēraklēs has to complete: slay the nine-headed Lernaean Hydra. The funny thing about this hydra is that no one is really sure how many heads it actually has. The generally accepted number is nine, but ten, or even a hundred are also mentioned. It's also unclear if there was only one head that was supposed to be immortal (as per Apollodorus) or if the creature itself was immortal. The sequence of events, however, is quite clear.
After his victory over the Nemean lion, Hēraklēs is send off to handle another sticky problem: the Lernaean Hydra, who was raised from the earth by Hera just to end the life of Hēraklēs. The Lernaean Hydra (Λερναία Ὕδρα) was the offspring of Typhon, and layered in the swampy lake of Lerna. Hyginus, in his Fabulae, describes the creature so:

"The nine-headed Lernaean Hydra. This monster was so poisonous that she killed men with her breath, and if anyone passed by when she was sleeping, he breathed her tracks and died in the greatest torment."
Diodorus Siculus, in his 'Library of History' has a slightly different view of the Hydra:
"The second Labour which he undertook was the slaying of the Lernaean hydra, springing from whose single body were fashioned a hundred necks, each bearing the head of a serpent. And when one head was cut off, the place where it was severed put forth two others; for this reason it was considered to be invincible, and with good reason, since the part of it which was subdued sent forth a two-fold assistance in its place."
No matter the description, it's clear that Hēraklēs is in for a rough ride. He realizes he needs help for this labour, and asks it of his nephew Iolaus (Ἰόλαος). He is Hēraklēs' charioteer, and was widely considered his lover as well. Hēraklēs sees in him a perfect aid and together they device a plan. From Diodorus:
"Against a thing so difficult to manage as this Heracles devised an ingenious scheme and commanded Iolaüs to sear with a burning brand the part which had been severed, in order to check the flow of the blood."
Now ready to face his adversary, Hēraklēs steels his resolve, and sets out in his quest. I'm going to let Apollodorus recount the entire labour. From his Library:
"...mounting a chariot driven by Iolaus, he came to Lerna, and having halted his horses, he discovered the hydra on a hill beside the springs of the Amymone, where was its den. By pelting it with fiery shafts he forced it to come out, and in the act of doing so he seized and held it fast. But the hydra wound itself about one of his feet and clung to him. Nor could he effect anything by smashing its heads with his club, for as fast as one head was smashed there grew up two. A huge crab also came to the help of the hydra by biting his foot. So he killed it, and in his turn called for help on Iolaus who, by setting fire to a piece of the neighboring wood and burning the roots of the heads with the brands, prevented them from sprouting. Having thus got the better of the sprouting heads, he chopped off the immortal head, and buried it, and put a heavy rock on it, beside the road that leads through Lerna to Elaeus. But the body of the hydra he slit up and dipped his arrows in the gall."

And so, Hēraklēs is victorious once more. On top of that, he now has poisonous arrows, which create wounds that do not heal. The crab that Apollodorus describes, by the way, ends up as the constellation Cancer.

When Hēraklēs returns to Eurystheus after completing the labour, the king scorns him for requiring assistance. He decrees that, because Hēraklēs could not have completed the labour without the help of Iolaus, the labour will not count against his total, and he will have to do an extra one to fulfill his debt. Enraged, but unable to make demands of the king, Hēraklēs agrees, and starts preparing his next labour: capturing the golden hind of Artemis.

Image source: Hēraklēs and the hydra