You may also want to click on the "AMR" below and retrieve a nice summary of the basics of the major doctrines as I saw in another thread you were new to Calvinism and were writing some basic things up.
Man's responsibility and freedom of will, are only protected by the sovereignty of God.
The most consistent atheists - including the Marxists - have always been determinists.
We don't know how a sovereign God maintains Man's metaphysical freedom and responsibility but because He is omniscient, omnipotent and omnipresent He is able to do it.
Unsaved men are of course ethically bound by sin. See the Westminster Confession of Faith Chapter IX.
If we live in a godless universe Man is not free and responsible, but all his actions are determined as if he were an accidental puppet of fate or chance.
The further people depart from the teaching of a totally sovereign God, the more open to question Man's freedom and responsibilty come. The less sovereign God is, the more open to determination by chance and fate, Man's will is.
I would warn against trying to fully sus out all the logic of God's full and utter sovereignty, along with our own responsibility for sin. It is a paradox that our fallen minds cannot fully come to grips with. Not that I'm saying don't think about it though .