I'll try and explain this as best i can, from what i know. Note i put these '.....' around words that aren't technically correct, but are a lot simpler to use.
In hyperspace (the 'region' outside of this universe's space/time) two things called membranes (i don't understand these at all!) collided creating a singularity. The moment it is formed the singularity instantly 'jumps' into its own dimension and creates its own space and time. (side note, theoretically it is possible to create a singularity in the lab, in which case it too would leave our universe)
The singularity then 'exploded' in the big bang creating first pure energy which rapidly formed matter and antimatter, matter eliminated all the antimatter but there was some matter left. (side note, it is perfectly possible that in other universes antimatter eliminated matter, it all depends on which was most numourous).
Strings became quarks, quarks became particles and particles became hydrogen. From hydrogen and helium, which is in essence two hydrogens combined, we get star formation. From dead stars we get second generation stars and planets, on planets we get chemical reactions, from chemical reactions we get proto-life which eventually becomes some form of life. All life we know is carbon based, but this is not necessarily the only way it can be.
I probably got some of that wrong, but since noone else has had a go explaining it in their own words, i thought i'd give it a shot.