Some truly great posts here, both detailed and accurate (depending on what side of the fence you're standing) but allow me in the most simplistic terms to explain how I see it.
Britain had a referendum and that went approximately 52% to 48% in favour of leaving.
Using the broadest of brush strokes I believe the two major factors in the vote outcome were the requirements of the British population to retake control of their borders and to have the age old right to create and be governed by their own laws.
There are more than ample examples of media involvement and hype out there regarding hard, soft or whatever kind of Brexit we will witness.
My main concern is the potential 'punishment' often made reference to toward the UK when she (as the PM has recently admitted ) leaves the Single Market. The threat of added tariffs/financial penalties etc.
The UK imports more from the EU than she exports and should said tariffs be imposed, a mirrored response would no doubt be the immediate result/consequence and I can't see BMW or Mercedes car workers (as an example) warming to Merkel for allowing this to happen. You could of course site a great many industries to the same test.
I truly believe that common sense will prevail in the end because neither side will benefit as a result and in addition, would only serve as further proof to those larger economic players in the world (Russia, China, America) just how poorly prepared western Europe are to defend themselves economically and possibly even militarily.
The UK has steadfastly maintained that her wish is to remain in close contact both economically and militarily with her friends and allies in Europe but that does not include membership of the union.