Actually, (and I'm not a biologist or biochemist so I may not be up to date on this) I think that scientists are still working on just the first step in such a process, namely the production of organic compounds from materials likely to be available on the early earth. I don't think that there's been a whole lot of serious research on the other intermediate steps that would be necessary to go from organic compounds to living cells. This is an obvious starting point for abiogenesis research, since if it could be shown that the formation of the necessary organic compounds could not have happened in the first place then there's no reason to even consider the other steps necessary to produce life. Of course, like I said, there may very well be research into the other intermediate steps that I am unfamiliar with.
There are a lot of interesting chemistry and biochemistry issues involved in this. My favorite, and one I'm surprised no one has mentioned yet, is the chirality of the amino acids, and other complicated organics, in living things.