Open the music file you want to change with any audio editing software that you have. If you don't have any software, there are plenty of free programs available on the Internet. Audacity is the most usable and gives the best results.
Make sure that the track you open has been recorded in stereo sound. You easily can tell if a track has been recorded in stereo by looking at the audio waves of the recording. If there are two lines of waves, then the song is in stereo. If there is only one line of audio waves, the song is in mono, and the lyrics cannot be removed.
Select the whole right side of the stereo track. With all music editing programs, the right stereo channel is the bottom line of waves, and the left stereo channel is always the top line of waves. To select the whole right channel, click and drag from the beginning of the track to the end.
Inverse the right stereo channel. Most audio editing programs hide this option in the "Effects" or "Edit" menus. With Audacity, select "Effects" and "Invert." The right stereo channel changes slightly, so don't be worried if the waves don't change significantly.
Convert both stereo channels into a mono output. Some audio programs store this option in the "Edit" menu, others hide the option in the "Properties" menu. If you are unsure, consult the product manual.
Save your new instrumental music file. Ensure that you don't overwrite your original file so that you have both versions of the song.