If you want to move forward, the back two motors spin faster and the front two motors spin slower. This tilts the aircraft forward and vectors the thrust in that direction. If you want to roll then the same principle applies but on the lateral sides. If you want to yaw, then you must understand angular torque. A spinning object will produce torque proportional to the speed with which it is spinning. That is why on traditional helicopters you see a main rotor and a tail rotor. If the main rotor is spinning counter clockwise, the entire aircraft will want to spin clockwise to conserve angular momentum. That is why the tail rotor is necessary, it produces the necessary thrust to counteract the forces of the angular momentum.
So in a quadcopter, each of the motors are configured such that they cancel one of the others out. So when you want to yaw (turn right or left), then two motors across from each other diagonally will reduce their speed, and the other two across from each other will increase theirs. This maintains the lift necessary to maintain altitude, but imparts angular torque to the aircraft which makes it turn. Now it would be impossible for a human to calculate exactly how much change in RPM to impart to a quadctopers individual motors to maintain control, so these calculations are carried out by a flight control board. This board is usually equipped with pyrometers and sometimes accelerometers. It has software that controls the motors based on the position of the aircraft, and user inputs from the transmitter.
So that may all sound pretty complicated, but don’t be scared because all that complicated stuff is handled in the flight control board. All you have to worry about it moving two sticks one way or another. So which quadcopter will help you get off the ground quickest? One of my all time favorite quadcopters for beginners is the Syma X1. It is very inexpensive and flies very well. It comes with a 2.4 GHz transmitter so you are able to fly outdoors and get pretty good range. Another good beginner quadcopter is the Blade mQX. This is a great little quadcopter as well and one nice thing is that it is compatible with other radios so you don’t have to rely on the one it came with. Both are durable and will provide you with hours of fun flying time.