Plug your headphones into the computer audio out jack (green for speakers on the back or a front port labelled headphones). The VGA cable doesn't carry audio and you do not have an audio in port for bringing that signal to the monitor.
The headphone jack is useful if you are using a video source like a Blu-ray player with an HDMI cable. Then you can listen to the audio.
I wish that I better news for you. The manual for the LG E2350 is available from LG:
http://www.lg.com/us/computer-products/monitors/LG-led-monitor-E2350V-SN.jsp . Click on the Support tab and look on the right side of the page.
Cindy Wells
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