Connect the 1/8-in. stereo mini-plug end of your adapter to the green jack on your computer's sound card. This jack provides stereo output from your sound card and will be the main audio source for your computer unless you have added a more sophisticated interface. In this case, your manufacturer's instructions will advise you of the recommended connection.
Connect the 1/4-in. phone plugs to each nearfield monitor, if these monitors are active, meaning that they have amplifiers built-in to drive the speakers. Active monitors require power cables as well as audio cables. If you are using passive speakers, direct your phone plugs to an amplifier and follow the manufacturer's instructions to connect your speakers.
Arrange your speakers approximately 3 ft. apart, centered on either side of the mix position. The speakers should point inward to the mix position, at about the head height of the engineer. Ideally, the tweeters will be at ear level or tilted down to provide a direct path to the ears, as high frequency information is the most directional.