(In Cubase: Right click on the track and chose “Stereo Flip” and then “Subtract”) Im sure its some similar ways in other similar programs.

Explanation:
So far you have substracted your stereo file. In other words you removed everything thats 100% equally panned to the left and the right side. In most productions you will find vocals, bass and kick in the center. This means you also removed some stuff that you did not intend to remove. Therefore, continue:

4. Use your duplicated version of the original track and put a high cut on the track to keep only the information below the vocals frequency range (this range will vary but you will easily hear when the vocal starts to disappear)

An example of how this could look:

This will leave you with some of the information from the bass and the kick. However you lost some as well.

This method is not perfect as you will both loose some stuff that you would want to keep, and you will keep some details from the vocals (ie. reverberation and all vocals thats panned differently). However, this is probably as close as you will get without getting the instrumental from the artist himself.

Hope this helps, feel free to ask if anything is unclear.