Cool, that's helpful, thanks. Is there something like a "Current Hypotheses of Abiogenesis for Dummies" kind of thing?
To put it in a nutshell off the top of my head
1: Various base organic compounds form on the surface of the Earth and Mars, before it had any noticible oxygen. Certain compounds, and variations of these compounds, dominate from the get go due to better stability. Also note that some of these compounds possibly originated from cometary matter.
2: Some of these compounds form more complex structures, such as lipid bubbles, protein chains, base chains, etc.
3: On either Earth, Mars, or both, some of these chains developed the ability to completely self-replicate in varying situations. This is sometimes called the "Pre-RNA World hypothesis" or "PNA World". Currently, it's the most hypothetical part of this.
4: Eventually, one of these chains formed RNA. Either it got sent to Earth from Mars, or developed on Earth independantly. For one reason or another, RNA overtakes all other biological attempts on the planet, forming the "RNA World" hypothesis, though to my knowledge this is supported by chemical analysis of geological strata.
5: Eventually, a piece of RNA lost an oxygen atom and became DNA. It may have taken a few tries before the result actually worked, but once it did, it overtook the planet.
I'm sure people with more biology experience than me would be dissapointed in my explanation - as I'm aware, the actual process involves hundreds of steps, some of which can occur without others and can occur simultaniously but are still necessary for -our- form of life.