I did this a couple of years ago with a cheap (£5) RC Lamborghini I bought from a supermarket.
To start with, I dismantled the remote control and located the switches that made it go forward/backward/left/right.
I then soldered wires onto each side of each switch, the other end of these wires I connected to octocouplers in a breadboard.
The other side of the octocouplers were wired into an Arduino - the octocouplers simply separate the two electronic circuits (Arduino and Remote) so you can control the switches on the remote from the Arduino without mixing the two circuits and all of the complications that go with that.
Finally, I wrote a small Arduino program that could receive commands over the serial port (USB) from the computer and control the appropriate switch depending upon the command received.
This enabled me to write simple Python scripts to send the required commands to the Arduino, meaning I didn't have to compile and upload new code to the Arduino every time I tweaked what I wanted the car to do.
You can see the result here:
I did this with very basic electronics knowledge, though if you don't have any experience in programming, you'll likely struggle with the software side of things.