Apparently traditionally when a young Ferengi goes out into the world, he sells off his treasured possessions to raise capital, and Nog is leaving for the academy. Also, Quark's cousin has finally coughed up a ship which has been owed to him for the last ten years. Rom checks it out and declares it safe, much to Quark's surprise and delight. For the test flight, they decide to take Nog to Earth. Quark leaves Morn in charge of the bar, and Odo observes that Quark's surprisingly generous taking Nog all the way to Earth. Nog and Jake are hanging out on the Promenade for one last time, when O'Brien and Bashir present the young Ferengi with a guidebook to Earth. The ship, now dubbed "Quark's Treasure", sets off, with Bashir noting no one's warned Earth they're coming.
During the voyage, Rom notices the cargo which Quark is smuggling, and Rom and Nog demand a percentage of the profits for their silence. As they approach the Earth's system, Nog finds something in his guide that excites him - Earth's historical figure Gabriel Bell looks exactly like Sisko. Quark says all humans look the same. Unfortunately Rom discovers the ship's been sabotaged so it won't come out of warp - he uses some trick with Quark's cargo, and the three wake up in some sort of military lab in 1947.
Yep, they crashed in Roswell and were promptly spirited off by the military.
Unfortunately their universal translators are broken, so they can't even communicate. Rom speculates that they're in the afterlife, but Quark pishes the idea. Initial attempts at communication do not go well, and Quark observes that 20th century humans are very stupid.
After some discussion, Rom thinks the problem is interference from atmospheric nukes. He borrows a hairpin from a nurse and pokes Nog's translator. Quark observes the humans smoking, and says if they'll buy poison to smoke, they'll buy anything. Finally Rom gets the universal translator fixed, and Quark announces to the humans that he has a business proposition for them.
General Denning is not convinced that Quark's just there to do business, but goes to get clearance from the President. Eventually the three Ferengi are left alone, except for the German Shepard, which turns into Odo, who'd stowed away on the ship. Rom has a plan for getting back to the future. Sheesh, it should be him joining Star Fleet - he's clearly the brains of the group. Quark's intent on staying so he can set up a Ferengi financial empire, but Odo informs him they're leaving and he's coming too.
The humans, however, have decided to change methods, and take the three Ferengi for interrogation. Sodium Pentathol is not effective on Ferengis. No surprise there. Nog switches to a story about an alien invasion and, with the help of the nurse and a scientist, the trio are able to escape. Odo helps them get past General Denning, and they take off in Quark's ship.
Enacting Rom's plan, they fly the ship into an exploding nuke and arrive back in the future. Odo, Quark and Rom return to DS9, where Odo promptly arrests Quark for smuggling.