In Space there is no air to put thrust on any other thing to expect any action-reaction forces. Then how do spacecraft go left or right or are the ineligible to take sharp moves?
Very good question!
In Space there is no air to put thrust on any other thing to expect any action-reaction forces.
You are right, there is not much to push on. In low Earth orbit there is a very tiny amount of air left. It's not very useful to use to maneuver much, but it's enough to gradually lower the orbits of anything up there.
So orbiting spacecraft use rocket engines, sometimes called thrusters or boosters to give themselves a push back up.
And you are right that they need action-reaction. The exhaust gas coming out of the engine is light, but it's moving extremely fast! That action is enough to give the spacecraft the desired small reaction.
There is however Earth's magnetic field. It can't be used to change direction or steer, but it can be used to put a torque on the spacecraft to change the direction its pointing.
In other words, it can't be used to change the trajectory but it can be used to change the attitude.
In deep space like going to another planet, there's no more drag really, and they still use rocket engines to change their trajectory.
Then how do spacecraft go left or right or are the ineligible to take sharp moves?
Giant rockets are needed to put spacecraft out into deep space; 95 to 99% of the mass of a mission is fuel, so the last bit of fuel you can bring with you to deep space is very precious indeed!
Spacecraft don't and can't make sharp moves. Their trajectories are quite slow, smooth and graceful, except for extreme cases when you need to loose a lot of speed to fall into orbit around a planet. Then the spacecraft spends a LOT of fuel all at once to try to slow down.
Instead, what mission planners do is spend a lot of time, years in fact, carefully planning the trajectory. They use gravity as a helper whenever possible.
For example Cassini flew past Venus, Earth and Jupiter on it's way to Saturn to make some somewhat-sharp moves and gain speed to get to Saturn in a reasonable time.
It then used a flyby of Saturn's moon Titan to make another "sharp move" and loose more energy to drop into a lower orbit around Saturn.
These deep space spacecraft need to be flying fuel tanks in order to get to where they want to go!
But what about Dawn?
The Dawn spacecraft demonstrated a new kind of engine using ion propulsion. This technology uses electric fields to accelerate its (ionized) gas to speeds much higher than a chemical engine can. Dawn's exhaust speed was about 30,000 meters per second, or roughly 10x faster than deep space engines can achieve.
This allows the same mass of fuel to make much larger changes in trajectory. However, the rate of gas flow is much, much lower than for traditional chemical engines, so what might take a few minutes or hours for them takes months or years.
So even though the change in trajectory is big, it is very gradual, and not a "sharp move". Dawn basically spiraled out away from the Sun by years of continuous running of its ion engine.
Still, Dawn used a gravitational assist flyby of Mars on its way out!
Trajectory of the Dawn space probe as of September 2009 source
above: "Engineers and technicians at JPL work to complete the stacking assembly of the Cassini spacecraft in 1996." From here. Ken Lubas / Los Angeles Times