What is the best software to use to extract the instrumental/background music from a song?

Unfortunately, it's just technically / physically / theoretically impossible to extract something from fully mixed audio. However, there are some simple techniques you can use to try to isolate vocal or other instruments that are placed exactly in the middle. For instance http://manual.audacityteam.org/o/man/tutorial_vocal_removal_and_isolation.html - the solution by Audacity software. But  do not expect quality results.

In order to extract music instrumental in the background, requires wave editing of a song. You might want to try Sound Forge or Gold Wave software which are good at wave editing. In Gold Wave, there are quick macros available to suppress vocals up to some extent. So, even if you've 80% of the vocals cut by the software, then you may reduce 20% manually by going over each vocal piece in wave editor.