The word you're looking for is abiogenesis. Use that to look for writing by people who know what they're doing,
But here's a quick, probably inaccurate starter.
Proteins are chains of amino acids. Amino acids can form naturally under early Earth conditions, they're relatively simple molecules. Proteins can work as catalysts, helping the formation of certain other molecules. A protein could have formed that worked as a catalyst for (proteins similar to) itself and built up from there. It's not very likely to happen, unless you have all the world's oceans to work with for half a billion years or so, in which case it might be.
Basic lipid cell membranes are known to occur naturally and assemble into a cell-like shape, so that innovation is inexpensive.