I can think of 2 ways:
(1) Open it up, get rid of off the control board in the quad and only keep the motors and electronic speed controller. There should one per motor, but they might be integrated in the main board in which case you'd have to get some yourselves. Then get anarduino (a programmable microcontroller) to control the motors. The communication with a laptop can then be done via an RF signals (using e.g. xbees) and use another arduino as a transmitter plugged into your laptop to control it.
There a lots of tutorials and blogs online about this kind of projects, with open source code available etc.
(2) Probably the easiest option: Reverse engineering the RF signals between the quad and the remote control and replicate them from your laptop. To do that, you'll have to know the frequency that's being used (probably written at the back of the remote), buy a receiver + transmitter for that frequency. Use the receiver to "listen" to what the signals are when using the remote. Then you can try to recreate those signals in software and use the transmitter to send those across to the quad.
Sounds difficult, but it's probably the easiest option. See this magpi article - page 8 that describes how to do this - This was for a totally different project but the method still stands.