We elect parliamentarians, who's job it is to took at the issues and make decisions. They've managed for every other major issue we've faced so far, even taking us into war. For an interesting take on this by Professor Richard Dawkins, see Richard Dawkins: Ignoramuses should have no say on our EU membership—and that includes me
But, as you say, we have voted to leave the EU. But what exactly does that mean? My preferred option would be the Norwegian model, where we continue to be a member of the Single Market, contribute to the EU Budget, and maintain the principle of free movement. In other words, exactly the same as now, but without the influence. (Apparently the reason Norway takes this approach is to be exempt from the Common Fisheries Policy. We could do similarly once out - great for our fishermen). In a way, I like this approach. We can be 'out', yet as far as the rest of the EU is concerned, due to lack of influence, we won't be able to make to make things difficult for the rest of them.
However, I don't know what will be negotiated or agreed, as we weren't asked in the referendum. No dount as soon as I am told, I will 'deal with it'.