If you're in the audio business, eventually some one is going to ask you if you can record them singing or rapping over some pre-produced music. It might be someone with karaoke dreams, a student making an audition track, or more likely a hip-hopper with some talent at beat making but who is lacking know how on getting good recordings of actual sound. Any of the above are usually worth working with. It might take a little work to get things together but it's not too hard to make someone's day, it's a couple extra bucks, and hey... it's only one mic right?
I'll leave out all the bits about getting good takes out of inexperienced vocalists and people that want to rap right over top of Jay-Z. Assuming there's no nonsense involved you may still have a good sized issue to deal with here. Some pre-produced backing tracks are intended to have a voice recorded over them. There's a whole industry based around making karaoke tracks, and some artists release music only versions of their songs (or they can be had dishonestly if you search the internet enough).
But the situation I'm talking about is the beat builders, I guess they call themselves "producers" these days that have musical talent but aren't so skilled at engineering a song. Putting together a piece of music where the vocals are important means leaving space for them to exist. You can find endless discussions and posts about carving out guitar tracks and whatnot to make room for the vocals.
So what do you do when presented with a stereo mix that's bangin' loud and doesn't have any room left in it for the kid to rap?
My technique involves a little side chain compression. I'll divide the track up into three bands, much like I do when setting up crossovers for a PA. That means duplicating the track a couple times, high pass one, low pass another, and do both to the last (just the mids are left). The bass can pretty much be left alone unless it's really going to step on things. The highs may or may not need attention, if they're really busy you may need to touch them but to start just leave them alone. The meat and potatoes of the mids is where this trick will be most effective.
Set up a compressor on the mid track and key it with the vocals you recorded. When there's no voice, the track is left alone, when the singer or rapper is on the mic, the mids are being compressed. Make sure there's no make up gain, you're looking for straight reduction. If you're careful with your attack and release settings you can make it pretty transparent. Dial the threshold and ratio in properly and you'll find that you can make the music gently step aside for the lyrics.
If the consonants aren't getting through then you repeat the process with the highs. You may find that you need to automate some of the settings. What works in a hard driving chorus might not work in a laid back verse.
Give it a try Brethren of the Knob and Fader. The difference between slapping a vocal on top of a produced track and gently placing it inside is huge. People will hear it and once word gets around that you're the guy cutting the hot vocals, you can make a nice buck at it with very little work.