Ducking/Sidechain Compression
I use one of these I picked up used for $45:
http://www.behringer.com/EN/Products/MDX1600.aspx
I use the Aux bus on a mixer, inputting all the mics and then outputting into the sidechain input of channel one on the mdx1600. I connect the DJ laptop output into the channel 1 and 2 inputs, then connect the outputs to a stereo input on the mixer.
The compression effect will quiet the music when the mics are used. I use a very quick attack and release time and adjust the compression ratio to what sounds good (quieting but not choppy).
There is one trick to using the MDX1600. I put a dummy 1/4 plug into the channel 2 sidechain input. I couldn't get very much (if any) compression without it.
I've also done this in software, but it's a bit involved. It requires VST plugins,a host application (sequencing software), and a way to route sound in Windows.
You also have to get the Aux Bus into the computer as well as getting the music out. In other words, the hardware compressor is easier
Google these:
energyXT ($50 simple sequencing software)
ReaPlugs (free suite of VST Plugins)
VBCable (sound routing)