Well, let's do a little thumbnail sketch here.
Genesis 3:14-19, the cursing of the serpent and of woman and man, is one of the more ancient sections of the Hebrew Bible. You can tell that it is ancient poetry inserted into the later prose narrative (still ancient from our point of view) by its diction and meter which contrasts with the surrounding text.
The larger context of the story is El myth, with later overwritings by Yahwist editors.
For those unfamiliar with El worship and Yahwism, the oldest Biblical traditions are El-ist. The worship of El has parallels in ancient Ugaritic and Egyptian tradition.
El was the leader of the Heavenly Council, the chief of the gods, who were the "heavenly host", visible as the stars. From time to time, El and the other members of the Council and the lesser members of the host would visit earth.
Polytheistic El worship was later supplanted by henotheistic (our god is badder than your god) Yahweh worship among the Hebrews. Yahweh was a mountain-dwelling storm god who led his people to victory in battle, and Yahwism overtook El worship during the long transition from the nomadic period to the establishment of the settled state, which required quite a bit of war.
The El traditions survived, but got a little rewriting. In fact, in Exodus a little bit is added where Yahweh tells Moses that he is the El of Abraham, Isaac, and Jacob, but that he didn't reveal his true name until just then.
In Job, we see another ancient poem sandwiched in between later prose passages. There, God makes reference to his battle with Leviathan, the sea serpent, an El-istic tradition with Ugaritic parallels.
So here we have 2 different traditions of conflicts between El and a serpent:
1. The cursing of the land serpent by El.
2. The battle between El and the sea god Leviathan.
In El mythology, not only were the land serpent and Leviathan entirely separate, but both were unrelated to Satan (the accuser) who was a member of the Heavenly Council, one who conversed and wagered with El, as we see in Job.
Satan is not the vanquished Leviathan -- who gets a separate mention -- and certainly cannot be confused with the cursed and lowly land serpent.
However, by the time of Jesus, Judaism has been subject to the influences of Hellenism, gnosticism, and most importantly Zoroastrianism with its theology of the battle between the forces of darkness and the forces of light.
At that time, some Jews had come to identify Satan with the head of a Zoroastrian-like legion of darkness, an image with parallels in post-Hellenistic gnosticism which posited the need to remove the veil of a deceiver of darkness in order to move the soul toward the light of true wisdom.
The author of Revelation, writing sometime in the last 2 decades of the 1st century CE, appears to be a Jewish member of the Jesus movement who is heavily influenced by both of these (relative to his time) modern theological movements, as well as by the Hebrew doctrine of the coming of the Day of Wrath and the subsequent judgment of mankind and the earthly installation of the Kingdom of God. His theology would have been unrecognizable to the ancient nomadic El worshipers.
He writes a visionary text -- a genre which did not arise until the Yahwistic period -- in which he identifies Satan (now the spirit of darkness at battle with the light of God, no longer the argumentative member of the Heavenly Council which we see in Job) with the ancient dragon, the serpent.
Here, he is probably drawing more heavily on the tradition of Leviathan than of the land serpent, but it is likely that by that time all of these threads had already been conflated into a single idea among certain communities. (And by the way, the author of Revelation is extremely well-versed in the Hebrew Bible.)
But it is important to remember that this is a visionary work, which is self-consciously symbolic. It does not even pretend to describe real events, but rather a vision granted to the recipient which is the key to understanding for those initiated into the mystery or the community of believers.
Indeed, John takes the genre to extremes that would have made Ezekiel's head spin. In the dragon/serpent/Satan reference, he not only alludes to El's battle with Leviathan, but also the story of Leto and Python. In doing so, his purpose is to warn his audience of the battles between good and evil, light and darkness, the Jesus movement and the outside establishment, going on in their day and time, as well as their significance to the impending Day of Wrath and subsequent rule of God on Earth.
Now, that's not anywhere near as pat an answer as Radrook has, but I'm afraid it will have to suffice, since it is a much more accurate one.