Riker is having some sort of dinner party in his quarters, and making scrambled eggs. Not a lot of scrambled eggs considering there's five of them. Unfortunately only Worf is able to eat the results (Riker will obviously not be volunteering for cooking duties any time soon).
Then they detect a Federation shuttle and set course to intercept! Cue title sequence.
The shuttle they find is drifting in space, so they tractor it aboard to discover that it's one of their shuttles. One of their shuttles which is sitting in the shuttlebay right next to it, in fact. Within the shuttle they find another Captain Picard, unconscious, whom Pulaski drags to sick bay. The shuttle's batteries are flat, so they drag Geordi in because apparently no one else can hook it up to the Enterprise and repower it. The ship resumes course.
The first attempt to recharge the shuttle fails because the technobabble power is wrong, so they go to look for a power inverter. In sick bay, they try to bring Picard 2 around, and he almost karks it, in pretty much a repeat of the shuttle scene preceding it. Data and Geordi manage to power the shuttle up and discover the onboard clock is 6 hours ahead - it's from THE FUTURE! Or he's just set his clock wrong.
Pulaski successfully awakens Picard 2, though the only difference seems to be his eyes are open. Meanwhile, Geordi and Data show the log they've downloaded, which shows the Enterprise blowing up. There's a discussion about what they should do next and they decide to continue on course.
Pulkasi says as they approach the point of the time jump, Picard 2's body clock is sorting itself out. Troi says Picard 2 has a desperate need to leave the ship.
Later on, they still having detected anything unusual ahead, and Picard tries to question Picard 2 again. No! Don't touch the temporal duplicate! The Blinovitch Limitation Effect! After Picard storms out, Troi and Pulaski discuss his mental state. Pulaski thinks Picard may snap.
The shuttle, BTW, appears to be named El-Baz, presumably after Farouk El-Baz.
An energy vortex suddenly appears underneath the Enterprise and starts sucking it in.
Wait, why are they showing a clip from New Earth to demonstrate how they're showing new episodes of stuff? New Earth screened last year! They could at least show something from The Runaway Bride!
Troi says she feels a consciousness, and Riker thinks they're being probed. Picard tries to work out what they should do next. Eventually he decides they should split, but unfortunately the vortex has a firm grip and they stop the engines - and are promptly sucked in.
They launch a probe, which is promptly destroyed, then something zaps both Picards. They realise that the entity is focused on Picard. He decides he may have to leave the ship to allow it to escape.
Picard 2 is now more conscious and capable of speech. Picard releases him and they talk while walking towards the shuttlebay. Picard realises Picard 2 is locked into the sequence of events, and shoots him dead. They set course for the center of the vortex and successfully shoot out the other end. Picard 2 and the shuttle disappear. Teh end.