Calvin's relationship with religion and God are among the things Watterson describes less thorough in his strips. The ones that do bring up this theme are few and not very clear.
Calvin has not been given a specific Christian upbringing by his parents. Grace and evening prayers never take place in the cartoon. But, Calvin has somehow learnt that there is a God, and obviously accepts this. The fact that God exists and that he is almighty, fascinates the little boy, and sometimes he imagines himself being the almighty and exalted. At the same time God receives a lot of scolding from Calvin, when things do not go his way. Calvin would prefer that God ruled according to his wishes, something that God probably doesn't have any intentions to do.
Whether Calvin knows the ten commandments or not is hard to say, but the little six year old must be accused of having certain problems with a couple of these. To avoid being held responsible for his less positive actions, he makes up the most sophisticated, not to say incredible, lies. Everything between heaven and earth is blamed for what he has done, and often "everything between heaven and earth" means Hobbes.