I'm not exactly an audio maven but here's what I
think will work. Look at page 21 of the mixer manual
here.
1. Each computer's audio goes into one of the input areas on the mixer. On the diagram they have guitars, mics etc in this area. The cable you will need deppends on the computers invlved though 1/8" stereo to 1/4" connections should work. Someone else may be able to answer whether an XLR connection would be better. Each computer goes into a different channel.
2. To connect the speakers use the outpput channels at the top right of the mixer. It is listed as powered speakers in the diagram I linked to above. Those connections appear to be 1/4" on the mixer so
this cable
should work. If it is the smaller 1/8" connector (headphone juack size) it's
this one (One per speaker).
It may take some fiddling with the knobs and settings to get things working. Start with the volume/sound levels low so some horrible distortion/feedback doesn't cause problems.
The cables I linked to come from a company called B&H which does audio, video, and computer gear. It might be worth calling /emailling them with your question. They are usuually pretty helpful. I have no connection to them other than as a customer.