First off … kudo’s for scouting the place out. You just beat about 95% of the competition!
No need for pictures, sounds like as standard a club setup as standard comes. The 850 is a 4-channel mixer and has plenty of inputs (6x CD/Line and 2x phono I think), so there should be a channel free for you. Get a good quality RCA/RCA cable (don’t worry about gold plugs, sturdy cable is more important) and just plug your S4 like that. Run a 0 dB test before your gig so you have the levels set correctly and make sure the channel EQ on the 850 is set to neutral (12 o’clock). Then you can control the room with your master volume. Do they have a booth monitor that you intend to use? If so, it’s probably hooked up to the 850. Make sure you have access to the booth level knob while you are playing (better for your ears to don’t have it on full all the time, just when preparing for the mix and for the actual transition.
Hope that helps.
Greetinx and good luck monday, let us know how you did!