What's the best way to connect my xbox to a pc monitor with no speakers and still have sound?

First we need to know if the monitor has compatible Video In : Is it VGA, Composite, HDMI....

My easiest solution would be to use the composite plugs to get the audio (Red = Right White = Mono/Left) to a set of speakers with proper audio IN, then connect the yellow to the monitor.

Or you could use an optical audio out.....

If the monitor is VGA only, you're pretty much S.O.L.
If it's HDMI you're kinda SOL unless you have optical audio capability.

sorry...need more specific info for a more informative answer.