In short: In the primordial soup. Clay crystals are trapped inside amphiphilic vesicles. The crystals as they grow copy crystal defects across the layers, the defects confer the crystals specific catalytic properties, when they brake, they replicate the information. The vesicles self assemble by simple amphiphilic molecules of the primordial soup. The vesicle molecules are very fluid, moving dynamically out side the vesicles membrane. The crystals polymerize other little molecules of the primordial soup that enter the vesicle. The polymers increase the osmotic pressure, stretching the membrane, resulting in a shift of the dynamic equilibrium of membrane molecules from the less stretch neighbours, to the stretched ones. They cannibalize each other. When they become too big, the vesicles split randomly in daughter vesicles. The system "reproduced", natural selection start doing its thing. At some point the polymers replace the crystals, after a while we end up with RNA and proteins.
more details then you probably want to read
start reading at 2.0, in 1.0 i just explain biochemistry as intuitively as i could
http://thechurchofthequantumimmortal.bl ... er-16.html
So, compared with competing models you have read, how do i fare?