There are many ways to approach the enabling of your quadcopter platform. One way is to build it from scratch. However, in this case, you're going to use a well-known, affordable platform to make this task much simpler. You'll use the Parrot 2.0 quadcopter platform, available from many different online retailers. Here is an image of it:
One of the key advantages of using Parrot 2.0 is that it uses a standard WLAN access point as a control interface; your Raspberry Pi can easily access this to gain control. That's it! You've got your hardware platform.