Charles II did not have much of a role in the early parts of the Revolution or Civil Wars because he was too young. He was only 19 when his father was executed.
After that, however, he became at least the official leader of the Royalist forces in the remaining Civil Wars. However, he seems to me to have been more of a symbol or figurehead at that point because he was relatively young.
He was not able to return to power until he was 30 years old. He had to wait until Oliver Cromwell died and there was enough of a power vacuum in England for the Royalist forces to push back into power.
So, to me, Charles II did not do all that much. He only became leader because of his name and he wasn't even the one who led the troops into London after Cromwell's death.