Well, you'd need to have some basic a priori knowledge on unification theories and particle physics to begin to get an understanding of things. Carbon is made up of protons, neutrons, and electrons. Of those three particles, only electrons are elementary. Protons and neutrons are made up of quarks and gluons.
With respect to where particles came from out of the big bang, you need to realize that at the temperature around 10^10 kelvin, the basic forces of the universe had yet to decouple into what we know today. The breaking of symmetry is what gave us the particles we know today.
Really, without getting into subjects of baryogenesis, nucleogenesis, symmetry breaking, relativity, matter/antimatter asymmetry, Freidmann's cosmological models, Einstsin's field equations, and quantum theory -- and the mathematics to go along with them -- there's not much you can really understand. This stuff isn't in a language just anyone can read.
I'd try to explain things and stuff, but I just got released from the hospital today and am still doped up on considerable amounts of demerol and percocets, so I'll have to leave this for someone else to explain. Sorry.