There are rough guidelines on how to proceed, but the negotiation will be largely improvised. Estimates of how long it will take range from two years to a decade or more. For officials involved, it is a legal and political no man's land. One senior EU official said: "We are faced with a million mad questions and we won't have answers any time soon."
The goal is to unwind Britain's 43-year membership of the bloc, disentangle and sever the legacy of shared sovereignty, and then reshape the biggest single market on earth.
Three fundamental issues arise.
On substance, what political and commercial arrangements will Brexit Britain demand and will the EU accept them?
In execution, will the exit deal — the divorce and breaking of old obligations — be struck at the same time as a trade agreement covering post-Brexit trade? And if no, is a transition possible to ensure a soft landing?
Across the continent, markets, officials, presidents and prime ministers know that Britain and its former partners in the EU are embarking on a potentially dangerous political voyage, navigating largely in the dark.
"This decision could trigger an emotional rollercoaster right across Europe whose ultimate effects are impossible to predict," said John Bruton, the former Irish prime minister.
The process — options but no set course
To calm nerves in the immediate aftermath, EU leaders want to show there is a timely and orderly means to part ways. Speaking on behalf of EU leaders, Donald Tusk, the European Council president, said: "there will be no legal vacuum".
"Until the UK formally leaves the EU, EU law will continue to apply to and within the UK and by this I mean rights as well as obligations," he added. "All the procedures for the withdrawal of the UK from the EU are clear and set out in the treaties."
Lawyers in Whitehall and Brussels see two distinct tracks. The first is under Article 50 of the EU treaties — the so-called "exit clause" — which lays down a two-year renewable deadline for a country to leave.
A second track makes arrangements for future relations, from trade to co-operation on security or law enforcement. This is a more complex negotiation and, once agreed, harder to ratify. It requires unanimity and approval by more than 30 European, national and regional parliaments, possibly after national referendums.
There are alternatives. One is to attempt a divorce on British terms. The Leave campaign has outlined plans to legislate in the House of Commons to repeal some EU obligations immediately, while holding-off on invoking the Article 50 divorce clause to deprive the EU of leverage on timing.
Any unilateral steps would seriously raise tensions with the EU. Brussels is looking at options to retaliate, including suspending the privileges enjoyed by British companies under the single market. Sir Andrew Cahn, a former head of UK Trade and Investment, Britain's trade promotion body, said: "Acting unilaterally would throw the law of the land into uncertainty, and risk a tit-for-tat response from others. It could be a slippery slope to real chaos."
The political choices — a wait for answers
By law, nothing fundamental will change for British companies in the coming weeks, months and possibly years. The formal EU rupture is some time away.
But Britain has been thrown into political turmoil. David Cameron's decision to step down as prime minister triggers a Conservative party leadership race could take several months to play out. An early general election cannot be ruled out.
Mr Cameron made clear the decision on when to trigger Article 50 is for his successor. That means any formal EU negotiations will not start until the autumn at the earliest.
Technical work will begin at the level of officials on Friday. But no serious negotiation can start until Britain decides how it wants to conduct the divorce, and what arrangements it will request after the exit. The House of Commons will also have a say on any mandate to negotiate Brexit.
A vote that changes everything
A vote against the EU could also turn out to become a vote against the United Kingdom
Leave campaigners such as Michael Gove and Boris Johnson have advocated departing from the single market altogether and negotiating a bespoke trade deal with the EU. Some Labour MPs have said they would fight to stay in the single market as a non-EU member, even if it involves accepting free movement obligations and EU budget bills. Most MPs in the Commons supported Remain in the referendum. While that argument unfolds through 2016 and possibly beyond, Europe will sit tight.
"There will be no time for romantic visions. The Leave camp would have to face reality rather quickly," wrote Adam Lazowski, a law professor at the University of Westminster. "Although both sides have a lot to lose, it will be one against 27. It would not be the EU leaving the UK, but the other way round."
The conclusion, the transition and the risk of a hard landing
One of the biggest economic risks is a long wait between Britain's exit and new trade arrangements. Before the vote, Mr Tusk said if needed, cancelling UK treaty obligations would be "relatively easy" and take about two years. This would settle outstanding bills from the budget and spending projects, the legacy rights of expatriates around the EU and in Britain, and the withdrawal of British nationals from EU institutions.
But he added it would be "much more difficult" to negotiate a new relationship. That would take at least a further five years "without any guarantee of a success". France and Germany are open to starting such trade talks in parallel with divorce talks, but are unwilling to give any guarantee that the two deals would be rapidly concluded simultaneously — the ideal scenario for Britain.
"There will be a gap," said one diplomat intimately involved in planning. "It is unthinkable that a [trade] agreement would be in force after two years."
A hard landing would mean that Britain would be left relying on basic World Trade Organisation trading terms, with no privileged access to European markets for UK companies. A softer transition could be arranged, but it would require agreement among all the remaining 27 members.
If, for instance, EU member states rapidly agree a trade deal, it could be provisionally applied while the lengthy and unpredictable process of ratification begins at national level.
Another option is to temporarily revert to an established model — such as that forNorway — to give Britain full access to the single market while its new trade deal is pushed through. That may be impossible for a Brexit government; for several years it would live by EU rules it cannot influence, pay EU budget dues and accept free movement of workers — just the things many voters rejected in the referendum.
Backers of the victorious Leave campaign are optimistic that common sense will ultimately prevail. Daniel Hannan, one of the most influential Brexit thinkers, pointed in a EuroMoney interview to the example of Irish secession and its bloody birth and aftermath. "And yet here we are nearly 100 years on; we still have a common free movement zone, common social security claims, common voting rights, because it didn't suit either party to unpick that deal," he said.
Sceptics think the political omens are less auspicious. "There are no good options, no turning back," said one senior EU diplomat who will be closely involved in the talks. "The best we can hope for is an amicable divorce and a long-term relationship that is constructive, as opposed to bitter and dysfunctional."