Zetsu is a plant, grown from the First's and tailed beasts' chakra
This is, I think, closest to the truth. I don't know whether Zetsu was created by Madara, or whether Madara has simply started growing/cloning Zetsu. We do know that Zetsu is plant-like or maybe fungus-like. His appearance with the Venus-flytrap and his various "spore" techniques suggest this.
Here's Madara's plan, as best as I can understand it:
1) Fight Hashirama senju to obtain his DNA.
2) Fake his own death. Madara could easily have used a Zetsu clone here, like how Kisame did when fighting Killer Bee.
3) Use Hashirama's power on himself to gain Izanagi.
4) Grow a copy/clone of Hashirama.
5) Zetsu is a plant creature, so Hashirama's wood release power is special for growing/cloning/copying Zetsu.
6) Use the power of the tailed beasts to amplify Hashirama's power and grow hundreds of thousands of white Zetsu.
7) Use the huge army to conquer the world.
All these things are starting to look very related. Zetsu is the real weapon. Hashirama is the tool to grow new Zetsu. The tailed beasts are the energy to power the Hashirama clone. Akatsuki is a tool to collect the tailed beasts. Nagato and the Rinnegan were used to gain access to the demonic statue.
We've seen in the manga several times where a powerful ninja finds a young orphan or a child with special powers, and uses them as a weapon. Zabuza did this with Haku very early in the manga. Orochimaru did this with several people, especially Kimimaro and Kabuto. Somewhere along the line, Madara found Zetsu and realized his potential as a weapon. Zetsu has a plant-style chakra and can make some amazing clones/copies of himself. With enough wood release chakra, Madara can grow an army of them. Of course, he needs a tool to generate wood-release chakra (Hashirama) and a tool to generate huge amounts of power (tailed beasts).
Madara was exiled from the Uchiha and traveled the world for a time after Hashirama became the first hokage. During this time he could have found Zetsu and created his master plan. Coming back to fight Hashirama in the valley of the end was not for vengence, it was just a part of his plan. He used Zetsu to help him fake his own death and escape after having gotten some of Hashirama's DNA.
Madara/Tobi as we see him now may actually be a Zetsu clone. I don't know. This would explain why Itachi called him a "shell of his former self", but doesn't explain how he can do cool space/time jutsus or use Izanagi.
