There is a common misconception that spacecraft and satellites stay in orbit by 'escaping gravity', it is not the case. In a low earth orbit the force of gravity is a bit less but s till something like 90% of that on the surface of the earth.
The reason for the apparent lack of gravity is that the craft and everything inside it are in free-fall. You can achieve the same thing closer to earth by getting in an aircraft which follows a parabolic trajectory.
So if a satellite is constantly falling why doesn't it fall back to earth. The reason is simple but not very intuitive. To remain in orbit the craft needs a tangential velocity relative to the earth and because the earth is (roughly) spherical this tangential velocity tends to move it away from the earth's surface. In a stable orbit the movement away is exactly the same as the movement down due to gravity. Because there is virtually no drag in space it requires little or no energy to maintain this tangential speed as there is no overall change in momentum. The sum of the tangential velocity and the free fall towards earth is a circular (or more generally elliptical) orbit.
In addition the angular velocity associated with a stable orbit is proportional to the altitude or the orbit so a geostationary orbit corresponds to a particular altitude and changing the velocity changes the altitude.
If it helps to understand this you can think of the analogy of a tennis ball on a piece of elastic. Here the elastic is equivalent to gravity, if you just stretch the elastic (ie the thrust of a rocket) and let go then the ball will 'fall' back towards your hand. However if you swing the ball around fast enough then the angular velocity of the ball reaches equilibrium with the stretch on the elastic and the faster you spin it the more tension (and stretch) you get in the elastic. Of course there is quite a bit of friction in this system so you need to keep putting energy in to maintain equilibrium but in space these frictional losses pretty much disappear.
However where you do need a lot of energy is in accelerating the rocket to orbital velocity in the first place and this takes a lot more energy than getting to orbital height. In fact you can get most of the way into space for very little energy using a balloon but at this point you still aren't in orbit.