My guess is this;
It's going to make less difference than people think.
We will put in place trading agreements with other nations. We will put in place immigration agreements with other nations. In fact the main difference is that such agreements with be voluntary between states, and not forced upon them by the EU. Nobody is going to be stupid enough to make major decisions now whilst emotions still run high. When all the hubris and fuss has settled down and calm heads prevail the UK will - almost certainly - leave the EU. But I think a lot of what the EU does will be replicated by new agreements between the UK and the EU or it's component states. Tell me. What is the stop the UK "leaving" the EU, but signing treaties to accept virtually everything it stands for?
I seriously doubt it's in the interests of *anyone* to be parochial, awkward, aggressive and nationalistic. And that's Assuming we do leave the EU and don't immediately join it's successor or similar organisation and that Britain stands on her own. We may have "voted" to leave, but that doesn't actually bind the government to action, and it certainly doesn't bind future governments to action and it certainly doesn't stop individual counties (England, Scotland, Northern Ireland, Wales etc) from re-joining on their own and it absolutely, 100 percent totally doesn't stop us from signing reciprocal agreements and treaties that replicate the best bits of the EU.
Provided, that is, that everyone proceeds in good faith. And I think they will. We want their goods, they want our Money and vice-versa - we enjoy cordial relationships with all EU states and I don't think leaving the clique is going to change that.
My guess is that this will largely be a paperwork change. Assuming the whole thing doesn't come unglued now, and we don't end up joining a remarkably-similar (although hopefully rather less messy and labyrinthine) organisation that supersedes it.