You have a simple and a complex approach possible.
Simple would be 2 or 3 photocells with matching LEDs for illumination.
When the photocell on the right senses the dark line by sensing less light, it steers left. Most any microcontroller would work. Arduino Uno is easy to use.
If you have to use a camera, you will need more processing power. A Raspberry PI 2 is well supported and you can buy robot kits for them. Here is one that looks interesting:
http://www.dawnrobotics.co.uk/raspberry-pi-camera-robot-chassis-bundle/You will need everything in the bundle with the possible exception of the WiFi. So, a bit more than $200 and you would have everything you need with the shortest learning curve possible.