Arduino can not be programmed from Processing. Although they share a similar development environment and logic, they are different languages (Processing is based on Java, Arduino on C):

http://www.arduino.cc/en/Reference/Comparison

But communication is possible (not only from Processing but in general). Loaded with a special program like lib Firmata one can read and control the Arduino using a special protocol (i.e. via an USB or Bluetooth connection).

http://www.arduino.cc/en/Reference/Firmata
http://firmata.org/wiki/Main_Page

Another way to communicate is to use serial communication (which Firmata is based upon).

http://arduino.cc/en/Reference/Serial

More detailed information is available here:
http://www.arduino.cc/playground/Interfacing/Processing