An example of interstellar travel with the briefest of framing statements thrown in to handwave away the usual issues of faster-than-light travel:
Turner hunched down further into his chair. Reaching up, he checked his straps and gave them a little tug.
Reversion to realspace in ten seconds. All crew to deceleration stations.
Muttering quietly to himself Turner absentmindedly tugged on the already snug strap. This wasn't his first trip between systems but he never felt quite right during reversion. Something about dropping from many times the speed of light back into normal space put a twitch in his guts.
Reversion to realspace in 3.. 2.. 1. Reversion imminent.
Halfway between the moon and Mars, glittering like a jewel on black satin the device begins to spin up. In the circle of the gate a lightning storm of crackling energy arcs back and forth, distorting the view of the stars beyond. Impossible colors race back and forth across the bow of the gate as the tremendous energy causes ancient mechanisms to turn and pathways to arc and flare. In a no-time blink, a ship is there, returned to our universe from points beyond. The gate itself begins to spin down, its purpose fulfilled.
Entry into realspace complete. Ships status normal.
It wasn't that there was a moment that Turner could tell when he was in the jump and when he was back to the land of stars and sublight events. But his guts knew and churned away nervously as he undid the straps holding him into his deceleration chair.
"Another clean jump, eh Captain?"
Turner reached over and flicked the intercom switch. "Wish whoever had built those things had included some meds for the end of the flight."
"Haw haw, you got a grounder's gut, Cap. Just ain't cut out for the long runs." Turner bristled a bit at the slur but it was an old argument and he knew his part well.
"Yeah yeah and you got a spacers head, Jack. Empty as a nebula." Turner could hear Jack chuckle as the intercom clicked off. Free of his seat, he checked the readouts in front of him and saw green across the board. Time to hit the galley and get something to settle his stomach, he figured. Pushing off through the door hatch Turner thought he caught a brief blip of red on the proximity sensor. It wasn't there long enough to trigger a new contact warning from the computer. Probably just a stray burst of neutrinos or something futzing up the sensors. He'd check it out once his stomach was feeling more settled.
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There you go - aliens did it. From here we can have Things riding along into realspace from the gate, or we can have Turner's upset tummy be used later in the story to indicate that we've hopped between realspace and warp drive if we're at a spot where he's been captured by forces unknown. We have moved our characters between spots at the speed of plot without bogging down into the exact mechanics of how it works. Hell, you could drop the description of the gate entirely and focus on the physical effects on the crew. The jump/warp/hyper drive Just Works and off people go to the stars.
Same thing for teleportation mechanisms. In my opinion you can have them Just Work and write around any specifics pretty easily. Rarely is the story served by talking about the mechanics of an tech rather than just using it. I've read loads of sci-fi and speculating about how the cool inventions work is part of the fun for the reader. It's fine to try and learn about modern physics and how it affects what we know about the universe and how your tech could fit into it, but don't let that stop you from writing your story.