What should an astronaut push off from in open space in order to change his speed to maneuver?

To make a maneuver in space, you can only push off from some object or throw an object away from yourself. An object (or station) of mass m will begin to move at a speed v. According to the law of conservation of momentum, the cosmonaut will begin to move in the opposite direction with a speed V = – mv / M. You can return to the station only by pushing off from the next item, which may not be.
For belay, the astronauts fasten themselves to the station with a special rope. They also have backpacks with engines, which also work on the principle of pushing gases in one direction to start moving in the opposite direction.