How to connect a phone's camera to an Arduino?
That video shows a Bluetooth connection between the smartphone and the Arduino.

(A USB connection between the smartphone and the Arduino might be better in some ways).

details

If you want more information after watching a video like this, click the "show more" button underneath the video to see the details.
Those details clearly say "The Nexus S device connects to the IOIO board via Bluetooth, and uses the smartphone's camera in conjunction with OpenCV and the external IR sensors to control the vehicle."
Those details also include a link to
"Android Based Robotics".

The OpenCV image processing software runs on the smartphone. In this autonomous application, the image data never leaves the smartphone. The software on the smartphone reduces the image data to two integers -- the X,Y pixel location of the center of the green ball.

The Arduino and the Bluetooth link can easily handle a few integers at over 200 Hz. Neither one is suitable for handling live video data.

The Arduino could probably act as the controller.
The camera could send the X,Y pixel location of the green ball to the Arduino; while the Arduino collects all the other sensor data; then the Arduino could use that to decide what to do; then send the appropriate control signals to the motor drivers.

However, in this autonomous toy car it appears that the the smart phone acts as a controller.
The Arduino collects all the other sensor data, forwards that data to the smartphone; then software on the smart phone takes that data and the X,Y pixel location of the green ball; then the smartphone decides what motors need to turn; then the smartphone sends the appropriate commands to the Arduino, and the Arduino demultiplexes those commands to the motor drivers.

For even more details on building robots using smartphones and Arduino, see


"Android Based Robotics" ( http://www.socsci.uci.edu/~jkrichma/ABR/ ).
The Tinkernut video
"DIY Smartphone Controlled RC Car" ( https://www.youtube.com/watch?v=xsJ7176fLNw )
goes into more details of how to connect a smartphone to an Arduino via Bluetooth.
Android Based Robotics: ground robot manual
( https://groups.google.com/forum/#!topic/android-based-robotics/_H8Zmvbxx-M )
"Simple RC car for beginners (Android control via Bluetooth)"
( http://solderer.tv/cxemcar/ ) ( via http://english.cxem.net/ ).
Communicate with Your Arduino Through Android (using USB cable)
ArduinoCommander:
"Control your Arduino board from your Android device over Bluetooth, Ethernet or USB"