You’ll wake up somewhere else… as someone else, with Squall, Zell and Selphie playing as passive role (although clearly aware of events and capable of commenting in side-text boxes). Instead of your original party you’re now in control of Laguna, Kiros and Ward, whose stats and abilities should match those of Squall, Zell and Selphie, respectively. Any magics, abilities, GFs and junctions possessed by one character normally is passed on to the aforementioned corresponding character now. It’s also worth noting that any EXP and AP you gain in this sequence is retained by your other characters, but you can still flee, use Card, or Enc-None to avoid this trouble if you wish.
Head up through the first screen to find yourself in a field where some high foliage has been flattened to form a path. Continue through this screen and note that there’s a Cure draw point along the way, which you probably don’t need to bother with at this point in the game. Make your way to the next screen cross a stream by walking across a log, then continue on to yet another screen. If you get into a random encounter you’ll likely end up fighting Funguars and Geezards, the former of which are fond of casting Sleep and Fire while the latter are… well, incredibly weak, but drop Screws.
On the next screen the three strangers will talk amongst themselves, with Ward mentioning their purpose here, helpfully dating the events you’re witnessing. Laguna will mention "going home" to Deling City, which - along with their uniforms - identifies them as Galbadians, and the location - Timber - places this event eighteen years in the past. In the next screen you’ll find a vehicle and a Water draw point. Draw if you wish, then enter the vehicle and the sub par soldiers will take off.
They’ll disembark in Deling City, with Laguna proving himself a public menace thanks to his driving skills, after which he’ll be teased by his friends over his obsession with some "piano lady". You can either head up or right, but unless you fancy killing Red Bats in the sewers, there’s not reason to go up right now. That being the case, head right, run down a street, then enter the Galbadia Hotel on the third screen where you’ll find a Save Point, in case you’re getting anxious.
When you’re ready to move on, head downstairs to the right and talk to a waitress and note the dialogue options presented to you. One of them is in dark gray text, signifying Squall’s interference - looks like the present-day SeeDs aren’t just passive participants in this past event, after all. If you pick the gray option twice, the three AWOL Galbadians will mention feeling strange ever since Timber… around the same time the SeeDs were caught in a fit of fatigue and projected into these three. Curious. Picking the gray option a third time will cause Laguna to lash out against the strange influence, startling the waitress. Good fun.
Pick the second option (the exact wording changes if you pick the gray option) to take a seat, albeit briefly. After the three chat about Julia - the pianist who is the object of Laguna’s clumsy affection - boldly venture towards the piano to witness Laguna’s pathetic attempt at getting Julia’s attention. Watch the scenes that follow (where Squall comments quite a bit on Laguna’s buffoonery) then head upstairs and talk to the receptionist and ask Which is Julia’s room?. The events following will vary slightly depending on which (if either) version of Timber Maniacs you picked up in Balamb, with Laguna either falling asleep (if you picked up the version in the hotel) or not (if you picked up the one by the train, or neither). It’s a trivial detail, either way.
Afterwards you’ll be back with your main party, who all realize they experienced the same dream. Selphie is oddly the voice of reason, and since there’s nothing you can do about the odd occurrence they decide to focus on their mission for now and report it later.