I've seen more than a few stories like this one
suggesting a second referendum. But how is that supposed to work?
The Treaty of Lisbon provides the now famous Article 50. EU leaders have stated, categorically, unanimously, that they will not negotiate anything -- officially, unofficially, or even in restrooms -- unless and until the U.K. government invokes Article 50. Once invoked, there is no provision to stop a country's exit from the European Union. There is only the option to stall the exit, and that can only happen when every other member votes unanimously to hit the pause button. (Unlikely, at least not without major U.K. concessions.) Anything else requires a treaty change, an extremely unlikely event and with some understatement. Article 50 was explicitly designed with finality and irrevocability.
David Cameron and the EU agreed to particular policy changes ahead of the referendum. Those policy changes were presented to voters. U.K. voters decided to leave nonetheless. The first referendum was the second referendum. That was the deal, and voters rejected it.
If Parliament doesn't think that the voters' rejection was wise, Parliament is free to vote against invoking Article 50. That is a perfectly legal option. The European Union Referendum Act of 2015 only created an advisory referendum as a matter of law. Of course if Parliament ignores or rejects their majority viewpoint voters then have a powerful right of review at the next general election. As a variation, Parliament can decide to hold an early general election. The Liberal Democrats have already declared they will run on a manifesto to ignore the referendum result. If general election voters put the Liberal Democrats in power, that would be a different second referendum result. A newer mandate politically trumps an older mandate, they would argue (and they wouldn't be wrong). Any other party, or party coalition, is free to try the same.
There have been several ideas mooted like this one (a second referendum) that are fantasy and inoperable. Unless Parliament wants to call an early election, in my view the new Prime Minister (Theresa May probably) should invoke Article 50, ask for exactly the same deal Norway has (EEA membership), shake hands, and agree to an effective date of January 1, 2018. Done and dusted. That outcome honors the referendum result (leave the EU) but also protects the United Kingdom's national interests (including the preservation of the Kingdom itself -- Scotland would probably not fly away) to the maximum extent possible. It doesn't do a thing about EU/EEA migration, so the racists and xenophobes (in particular) will be upset. FINE. It's an outcome about 55% of the British public can support: the 48% who voted to remain, and another 7% of the voting public that did not vote to leave for migration-related reasons. May could also introduce whatever points system the government wants for non-EU/EEA migrants.