Turn off your computer and set up your chosen mixer in a convenient location for your personal operating convenience.
Plug in one male end of your 1/8-inch audio cable to the 1/8-inch audio output jack on the back of your mixer, and then route the cable to the rear of your computer. Connect the other male end of your audio cable to the 1/8-inch "Audio In" or "Line" jack of your computer's sound card, whichever jack you prefer.
Plug the mixer's power plug into the nearest wall outlet, and then plug in the XLR plug of your phantom-powered microphone into one of the round XLR jacks on the mixer. Most multichannel mixers have two or more channels with XLR jacks, so choose the one you desire to use with your microphone, and plug the mic into that jack.
Turn on the power switch of your microphone and double-check that the indicator lights come on as they should; then turn on your computer.
Use your favorite audio recording software to test your audio quality and audio levels, and adjust the mixer channels as necessary.