Could Vermont Really Secede from the Union?

A year an a half ago I went to a meeting in Vermont where people talked seriously about seceding from the Union. But I don't recall any discussion of what that would actually involve. The current conflict in the Ukraine over Crimea has put the issue of secession on the front page and the NYTimes has an op-ed on the subject: Sovereignty vs. Self-Rule: Crimea Reignites Battle. Here's a couple of paragraphs:

Of course, the fractiousness that has chopped up the Soviet empire into increasingly smaller and often dysfunctional pieces is not relegated only to that part of the world, although in the West in recent years it has played through political and legal processes rather than military ones.
In September, for example, Scotland will hold a referendum on secession, a vote being held with the acquiescence of London. In November, Catalonia plans its own vote on independence from Spain, although in that case the Madrid government has called it illegal. Quebec held unsuccessful referendums on independence from Canada in 1980 and 1995 and as recently as last week its separatist government was discussing whether another should be held.

I assume that a Vermont – or, for that matter, a Texas secession – secession would be more like Scotland or Quebec than like what's been happening with the former Soviet empire. Under what circumstances could that actually happen? How would the free republic of Vermont disentangle itself from the Federal system, the military, banking, and tax systems?