Hook up the computer to the stereo through the headphone jack. If the computer has a headphone jack and the stereo has an auxiliary input, this is the easiest route. Hook a male 1/8-inch to RCA adapter to the computer, and then run a set of RCA cables to the AUX input of the stereo. Turn the stereo on AUX and hit play on the computer. If your stereo has a 1/8-inch input jack (typically at the front of the stereo), buy a 1/8-inch male-to-male cable to hook them together.
Purchase a 1/8-inch tape adapter if your stereo lacks an AUX input, but has a tape player. Plug the male end into the computer's headphone jack and put the tape in the stereo. Select "Tape" as the source and press "Play" on the tape player.
Purchase a device that connects to the computer (usually through USB) and supplies a headphone jack or other connections to patch an audio signal if the computer lacks a headphone jack.
Use an HDMI cable if you have a computer with an HDMI output and a television or stereo with a HDMI input. The cable sends your computer's audio to the stereo using this cable.