so the approach now should be to pull together and try to make the best of what the majority wanted
But what does the majority want?
One obvious way out of this crisis - go to Europe and say we want to adopt the Norwegian model.
Except that that will mean agreeing to enact all EU laws. We've probably got exemptions that we'll lose as a result and basically become even more under the EU's thumb than we were (at least as far as the majority are concerned). So I cannot believe that is what the majority want even if it's what I hope happens (quickly). (And I think this would be an easy sell in Europe - they get the current benefits of the UK in the EU without the "valuable but difficult friend" issues we cause at the moment)
I've seen some claims that just discussing brexit with the EU ministers could now trigger Article 50. So maybe the above is what will have to happen while we find out what the majority really want and then try to negotiate it. That at least would settle the markets and give as much time as necessary to move forwards. Unfortunately I don't see how to move forwards from that so *everybody* will be unhappy because while a majority were in favour of being "out of Europe" I think the single largest minority are in favour of being in Europe and the "out of Europe" are such a disparity of views that each have a different no compromise issue that we'll never be able to decide on anything better than we've given up.
The mayor of Calais is (again) calling for the border to be moved to the UK (and the refugee camps - thousands of extra immigrants that this vote was supposedly supposed to stop. The UK no longer has a veto on Turkey joining the EU and IIUC, should the other 27 members decide to accept it and us adopting the Norwegian model then I don't think we'll be able to negotiate a temporary exemption to the free movement of Turkish citizens.