I loved Trek and Lost in Space when I was a boy. In many episodes of both shows they would encounter fantastic alien technology and figure it out before the last commercial break. I'm older and more jaded now and call bullshit.
Say, you took a brilliant Victorian type, Professor Moriarty, and gave him a Navy surplus nuclear submarine. Boom! He has nukes, he's master of the world. except he hasn't a clue how it works (manuals were lost in the temporal exchange, no refund, no exchange read your waiver!) Could he figure it out without killing himself or scuttling the ship? Would he cause a meltdown trying to find the coal bunker (I say, let's extricate these metal rods Colonel Moran and see why they were deemed to so precious as to be ensconced in this metallic vessel.) Okay maybe not that. He's certainly smart enough to read a warning label. Alien tech wouldn't even have labels we could read (What's this that looks like the Olympic symbol only in plaid pictographs? Meh, pull that gewgaw out of that thingawhatsit.)
Note malfunctioning alien tech is usually worth a whole movie or novel. Alien tech either works perfect or ushers in an apocalypse, or at least prematurely emails your letter of resignation to your boss telling what a tool they are. Alien tech never just loses your mp3 playlists or forgets a password.
But what could we learn from technology hundred ort thousands or even decades ahead of us? Take an example.
It emitted radio signals intermittently from 1899 to 1928 and was detected by Nicola Tesla and others. It was an anomaly and quickly lost in the shuffle of the First World War and only occasionally noted after.
In the forties the Third Reich knew something was there. There was discussion of sending a man atop a modified V-2 to investigate but defeat and partitioning got in the way. The men at Peenemunde knew the real reason rocket technology was so important to the Reich and took their stories to West ... and the East.
The Space Race was begun for national pride publicly. Few knew of the darker reason, a few hundred miles above there was technology that could change or end the world. Titov did a flyby in Vostok 2 followed by Glenn in Mercury 6. Both confirmed the theories and fears. It was there, it was big and there were what looked like running light s powered on. No response to light or radio signals. Later mission assed closer and provided tantalizing photos. Engines? Sensors? An airlock.
But the Gemini missions would be the first to put a man onboard the Black Knight.
The premise is simple but flexible. In the 60's-70's mankind discovers the first of several alien derelicts in his neighborhood. How advanced the tech is, and what can be understood can be nearly anything. In thirty years we might still be puzzling over how to open the airlock or we may have unlocked SECRETS. It could be relatively minor matters like material tech or a storehouse of fusion catalysts. You could have accelerated development with recognizable tech (Orion drive ships heading to explore Jupiter) or technology that's mostly handwavium but looks familiar (Lost in Space, Space 1999). Maybe mercury capsules become the first scoutships for the solar system with mini-warp drives fitted to the stern and when the ftl drive is figured out things get really crazy.
(The Gemini model is from the Sketch Up 3D Warehouse: Blue Gemini by Alistair D. Alien/Black Knight/enigma by yours truly.)