I am looking to write an Arduino script that uses whatever audio signal is going to the speakers to create a physical visualization.
The Arduino is connected to the windows machine only through USB, so I need to use USB to find out what is being sent to the speakers. How would I access this information?
As of right now, the Arduino can only communicate with the computer via serial over USB. Things have changed with the new Arduino Uno, but the examples have not yet been released to show how to have the new Arduino act as other USB devices.
You would have to write something for the Windows box that monitor's the system audio and sends the info about it over serial to the Arduino, as long as you want it to only connect via USB.
There is a Java library for processing called ESS that lets you access audio out.
There isn't a very good way to interface an audio signal to an Arduino without some external hardware.
One way to do it though would be to connect the audio line to a biased pin with a capacitor, then you could use the ADC directly. There will be pretty terrible dynamic range, but it only takes 3 passive parts. Running that through an opamp before going to the ADC pin could significantly improve dynamic range and provide a filtering opportunity (see below). Alternatively, you could switch on an on-chip voltage reference to use (typically 1-1.5 V) instead of the main supply.
It doesn't matter that much for a straight visualization, but the sample rate will not be good enough to capture the full spectral content of the audio (in addition to the poor dynamic range resolution). The default Arduino sample rate is 10 kHz(-ish...possibly asynchronous), so you will only get valid data if your signal is below 5 kHz, otherwise aliasing will muck it up. (If you write your own analog driver for the ATmega32P you could get up to 76 kHz sample rate with 8-bit samples)
Then to actually communicate that data to a computer, you can fairly easily throw all those ADC values onto the UART for the computer to pick up and process as it sees fit. An ATmega will not have the power to compute FFTs on the fly (what you'd do almost always do for a viz anyways).
Or to skip all that, connect the audio signal to your computer's sound card (or USB sound card...they're pretty nice) and use some audio driver.