They explained the process of secession in the Declaration of Independence. Madison also explained in the Federalist Papers how the states can secede if the tyrants at the federal level won't let them go:
"The only refuge left for those who prophesy the downfall of the State governments is the visionary supposition that the federal government may previously accumulate a military force for the projects of ambition. The reasonings contained in these papers must have been employed to little purpose indeed, if it could be necessary now to disprove the reality of this danger. That the people and the States should, for a sufficient period of time, elect an uninterupted succession of men ready to betray both; that the traitors should, throughout this period, uniformly and systematically pursue some fixed plan for the extension of the military establishment; that the governments and the people of the States should silently and patiently behold the gathering storm, and continue to supply the materials, until it should be prepared to burst on their own heads, must appear to every one more like the incoherent dreams of a delirious jealousy, or the misjudged exaggerations of a counterfeit zeal, than like the sober apprehensions of genuine patriotism. Extravagant as the supposition is, let it however be made. Let a regular army, fully equal to the resources of the country, be formed; and let it be entirely at the devotion of the federal government; still it would not be going too far to say, that the State governments, with the people on their side, would be able to repel the danger." [James Madison, Federalist Paper 41, in Bill Bailey, "The Complete Federalist Papers." The New Federalist Papers Project, p.219]
That was true in Madison's days; but by the time the tyrant Lincoln came along, there were too many entrenched federal (mostly Union) politicians who were more concerned with political patronage than the Constitution. Politicians are far more entrenched today. If you desire to become filty rich, but lack an appropriate skill set, consider running for Congress.
Mr. Kalamata
You are conflating the natural right of revolution with secession. These are two different things. Like apples and oranges. Right of revolution is extra-legal, secession is a legal act. Usually agreed upon by all parties and or with a process written into the organic law of the organization(for example the EU).