You’ve identified why spaceships don’t use propellers or jet engines…there’s no air. Propellers and jet engines push air so they only work in an atmosphere.

So instead you have to push off something. The most common way is to create a controlled explosion and shoot the expanding gases out a nozzle. Smaller releases of gas can be used to make smaller changes, like to point slightly to the left or right, or to start or stop rotation.

Once moving there’s no air to create drag so once you’re going as fast as you want to go you turn your engine off and just coast along. You’ll still be affected by gravity, so you have to account for that. And there is a small amount of gas even in mostly empty space.

For interstellar travel there’s a different proposed solution to the problem. You see in order to use exploding gases to accelerate you fast enough to make traveling to another star achievable within the lifetime of the astronauts you’d have to use a lot of fuel, and fuel is heavy, and takes even more fuel to carry into space. Instead you can deploy a large sail and catch the wind coming off of the sun or fired from a laser on earth, similar to how a sailboat catches the wind. That can get you going to 10% light speed. You’d reach the nearest star in just about 40 years! We’re still a little ways off from being able to construct a sail thin and light enough while still being strong. But we’ll get there soon.