Hello,
I am Malik, an experienced embedded system developer. Specialized in different kinds of embedded platforms like ARM, Rasp Pi, Arduino, PIC and 8051.
Your task is not as simple as to power up a motor through micro-controller (in your case Arduino). As you stated you need controlled moment of motors for a quadcopter. Besides the fact that you need only one moment, i-e, up and down (Take off and Land).
You must keep in mind in quadcopters we use brushless motors with high RPM, for this famous is A2217-9 Brushless Outrunner Motor. These three-phased brushless motor are controlled by the Electronic Speed Controller (ESC). The ESC has three pairs of wires: current supply(2 thick) / motor wires (3 thick) / controller wire (3 small).
Secondly, as the quadcopters are operated wirelessly, we will also need to code for RF communication, I will recommend to use 434MHz RF transmitter and receiver to get the job done.
There are number of factors involved in proper flight of a quadcopter but as you need simple takeoff and landing, I can give you robust solution keeping the cost minimum.
I will provide you complete documented Arduino code along with all the circuitry which will guide you how to assemble everything.
For further details, please contact me.
Regards.