How do Rockets Help You Maneuver in Orbit?
Speeding up and slowing down in orbit works just opposite to what you might expect. The larger a spacecraft's orbit, the slower the spacecraft travels. So if you wanted to pass a spacecraft just ahead of you, you would have to fire a thruster in a forward direction. This would decrease your orbital energy and drop you into a lower orbit, where you would travel faster! The "passing lane" in orbit is always lower.
How do Rockets Help You Maneuver in Open Space?
Once you are far from a planet, say, while flying between Earth and Jupiter, mid-course corrections are fairly straight-forward. To speed up, you fire a rear-facing thruster. To slow down, you fire a forward-facing thruster. To alter your course, you fire a thruster in a sideward direction. To rotate your spacecraft, you fire a pair of sideward-pointed thrusters located near opposite sides of the spacecraft. To stop rotating, you fire thrusters aimed in the opposite direction.