Summarize:

Most desktop and laptop computers use a 3.5 mm mini-jack, the type that's compatible with standard headphones and earbuds, for audio output. An HDMI port can also be used for audio output. The most common "audio in" port will be the red and white RCA (composite) jacks for an A/V connection. Other possible audio-in ports include:  3.5 mm mini-jack Digital optical audio S/PDIF digital audio Depending on your computer's output port and the TV's input port, you will need one of the following:  3.5 mm to 3.5 mm cable; 3.5 mm to RCA input cable; 3.5 mm to RCA adapter and RCA cable; 3.5 mm to Digital optical adapter and digital optical audio cable; 3.5 mm S/PDIF adapter and S/PDIF cable; HDMI to Digital optical adapter/extractor and digital optical audio cable; or HDMI to Digital S/PDIF adapter/extractor and S/PDIF audio cable If you're using an adapter/cable combination, connect the correct end of the cable to the adapter. If using an RCA cable, be sure to match the red and white connectors with the corresponding colors on the input. If using an RCA cable, be sure to match the red and white connectors with the corresponding colors on the input. Take note of the port number labeled on the TV.  It's a button on the remote or on the TV itself and is typically labeled "Input" or "Source." You should see a blank screen on the TV but hear the sounds generated by your computer over the TV's speakers. If you don't hear any sound: (1) Make sure the volume is up and mute is off on both the TV and your computer; and (2) Check your computer audio output or sound settings to make sure that the output is set to the headphone jack.
Locate the audio output jack on your computer. Locate an audio input port on your TV. Obtain the correct combination of adapters and/or cables. Connect the adapter or cable to your computer. Connect the correct end of the adapter or cable to the TV. Power on the TV and your computer, if you haven't already done so. Locate and press the input selector for the TV. Select the A/V port to which your computer is connected.