When you need to make Arduino communicate with your computer, you can use Firmata library. It is already in your Arduino IDE. Go to Example/Firmata and you will see a lot of example sketches.
If you want to get sensor input data or control digital output pins from your computer, you can just upload “standard firmata” sketch to your Arduino.
Now, if you want to control/get data in processing, open processing/ examples/ contributed libraries / arduino. You can find many example sketches to access analog/digital input pins, control digital output pins.. so on.
If you like to use PD (pure data), you can download PD from here >> http://puredata.info/downloads
Install PD on your computer as instructed. If you are using mac, you may need to install extra things.
Then download pduino library and example from here >> http://at.or.at/hans/pd/objects.html
it is called Pduino-0.5.zip
This is what Ylenia was using for her sound-jacket project.
There are also Firmata implementation on max/msp and vvvv.. so on.