eliminating all Dark Side users so that only the Light Side remains?
reducing the Dark Side's influence to almost nothing, but still leaving some Dark Side users so that there is a balance of energies? (End of Ep VI, there are still Dark Side users in EU)
creating an equal presence on both sides?
(for example, at the end of Ep III there are two Sith [Sidious and Vader] and two Jedi [Yoda and Obi-Wan])
Any other way not mentioned above?
In the commentary of A New Hope, G. Lucas said:
Which brings us up to the films 4, 5, and 6, in which Anakin's offspring redeem him and allow him to fulfill the prophecy where he brings balance to the Force by doing away with the Sith and getting rid of evil in the universe...
Which proves that balance does not mean equal number of Sith and Jedi.
The meaning of the prophecy is not totally clear, as noted by Yoda. But we still have some infos about it, for instance in Darth Plagueis:
Brazen and shameless, and at their own mortal peril, they had waged etheric war, anticipating that their own midi-chlorians, the Force’s proxy army, might marshal to boil their blood or stop the beating of their hearts. Risen out of themselves, discorporate and as a single entity, they had brought the power of their will to bear, asserting their sovereignty over the Force.
This shows the difference between a dark sider and a Sith Lord. A dark sider is a force sensitive individual using the dark side of the Force. A Sith Lord tries to put the Force itself,in all its aspects, to its service.
That's why the Force tried to destroy the Sith, as they are at war with the Force itself.
There were also some infos in the Clone Wars animated series during three episodes: Overlords, Altar of Mortis, Ghosts of Mortis. In those episodes, it is shown that the Light side and the Dark side are equally important part of the Force, both being necessary to the harmony of the galaxy.
In one episode Anakin must pass a test to show if he's the Chosen One: he does so by controlling both sides of the Force at the same time.
So it seems that in the Star Wars universe the dark side is not evil by nature (a position held by Vergere for instance), and that it's closer to a ying/yang situation, where harmony comes from balance between the two sides.
So the prophecy probably means that Anakin would bring harmony between the two sides of the Force, which requires the destruction of the Sith whose aim was to destroy the Light side.
It's interesting to see such an interpretation of the prophecy does not really corresponds to Jedi orthodoxy, especially during the post-Ruusan reformation, where the Jedi decided to cut themselves utterly from the Dark side by renouncing to any and all emotions.
Version of the Jedi code during Anakin's era:
There is no emotion, there is peace.
There is no ignorance, there is knowledge.
There is no passion, there is serenity.
(There is no chaos, there is harmony.)(*)
There is no death, there is the Force.
Emotion, yet peace.
Ignorance, yet knowledge.
Passion, yet serenity.
Chaos, yet harmony.
Death, yet the Force.
There is a huge difference during the two: one seeks balance, the other deny the very existence of the Dark side.
I would also note that as the Dark side leads to death (Korriban becoming a desert planet), this new version of the Order became sterile due to its rules against attachments. Looking at Anakin, who was the Force made flesh, it seems that the dark side (and so emotions) is as legitimate than the Light side as a part of the Force, and that balance means equilibrium between the sides, and not annihilation of one.
and did he fulfill the prophecy?
In G and T level canon yes, Lucas said it himself.
In C canon a good case can be made that he didn't, as the Sith came back.