1. Better known as the "Alcubierre Drive", Compress space infront of you and expand the space behind. Essentially inching forward like the inch worm. (If we presume that visually, the inch worm stays in the hunched position and slides forward because our eyes cannot see it's movement) Doing this smoothly in theory lets you accelerate and decelerate infinitely.
https://en.m.wikipedia.org/wiki/Alcubierre_drive
2. Warp space infront of you to create gravity, and pull you forward. Essentially, you make a pot hole in space time, and "fall" into it. This is basically the same Alcubierre Drive, but without the expansion at the rear.
2.1: One version holds that pothole at a specified distance infront of the ship.
2.2: The other version creates the pothole, then removes it before you reach it.
I know space is big and all that, but this seems like an irresponsible option.
I like to think that concepts such as "you must be at the edge of the solar system to initiate faster than light travel" or "cannot initiate faster than light within the gravity well of planet" originate here.
I have nothing to backup that theory of course.
As for space pollution, I never really thought of that. But considering some of our observation tools observe 'gravitational waves'? I could imagine another "starlink and light pollution is getting in the way of space observation" situation.
What that means is complicated to explain, but the gist of a warp drive is that you expand space behind you and compress space in front of you. The normal space in between gets pushed forward, ideally at speeds faster than light. There's lots of good explainers on YouTube if you want to learn more.