How can I control audio volume with Arduino?

Do you know how a [u]regular/manual potentiometer[/u] is wired-up?

[u]Digi-Key[/u] lists thousands of different digital pots (I'm sure they are not all in stock).

10k to 100k Ohms is a good value for line-level audio. You'll need two for stereo (or you can get a dual digital pot), but you can connect as many as you want to the same control-signals from the Arduino. You'll probably want to get a thru-hole package if you want to avoid soldering the smaller surface-mount parts.

Different digital pots are controlled differently, and it's your choice of how you want to do it. The most common method is serial I2C. There is an I2C library for the Arduino, so it shoudn't be too difficult. Some are controlled with a parallel (binary data) connection. Some have up/down digital controls, which might have an advantage in that you won't get a sudden full-volume blast if there's a little "glitch" i the control data.

An audio volume control has an "audio taper" (approximately logarithmic). This is because 50% on a regular (linear) pot sounds a lot closer to full-volume than half-volume (due to our logarithmic hearing). With a digital pot, this can be handled in your sketch.