If the South had a right to secede, where in the Constitution is the process outlined? How did the South attempt to follow said process? To me, it looks like they tried to force the issue with violence, firing the first shots. How did that work out for them?
The South lost. Get over it.
Where does the Constitution forbid it? The Constitution granted specified powers to a federal government. All others were retained by the states or the people. Several states, both north and south, stated in their ratification that they reserved the right to withdraw if things didn't work out. Congress accepted those ratifications. After the civil war, several amendments were passed (at bayonet point in the southern states). None of the amendments mentioned the right to secede, so the Constitution today still has no prohibition on secession.
I won't even get into the argument that if the Founding Fathers had a right to secede from the British Empire, how could their descendants not have that same right.