It will depend on your source and whether or not there is a clean centre channel. First step is to demux (separate) the audio and video to different streams. Some will have the music/sound effects/dialogue already separated, but that's rare.
If you go to the technical forums then there are several tutorials on how to do this. The easiest one to follow is probably Gemini's, which is specifically for preparing a HD source for editing:
https://forums.fanedit.org/showthread.php?tid=5592
There are lots of other similar threads on this very subject within the same part of the forum.
Once you've done this, changing volume levels of tracks should be pretty straightforward. If your centre channel isn't clean then that's another story.
Edit: In terms of what tools you might use on a non-clean track, you can use things like gates or EQ's to cut out certain frequencies. What you need to do will vary depending on the project. Best thing to do is just experiment with those sorts of tools and see what results you get. I'm sure there are others on the forum with a bit more experience in that area than me though who can advise.