The Vivitar 285:
Runs on batteries - AA, which are housed in a replaceable "pack" that you insert into the body of the flash.  you can buy these pack seperately so you can haver them all loaded - when it runs through the battery you just slip out the old on, and slip in the new on - think of it as a speed-loader method. Or it can run on external batteries (Quantum Batter 1+) with an adapting cable to hook them up - the end that goers into the 285 is shaped exactly like the battery pack.
The radio slaves connect to the camera on the hot-shoe, and have connections for you to plug in cables - which is what will go out to the light.

There are a HUGE multitude of cables you can buy - just go into any pro camera shop and tell them you need to connect "this" to "that" and they'll either pull out the correct cable for you, or can order it very easily.
Flash sync is mostly camera-specific. Most camera shutters sync at 60th of a second - most new DSLRs can sync above 125th second. Some can sync higher - any LEAF SHUTTER LENS can sync to it's highest speed labeled.

I've fired the Vivitar and my Metz or shots with my Mamiya RZ at 400th sec and they came out perfectly - because most flashes' burst rates are faster than 800th sec. What you usually read in the flash specs is "duration" (THIS one has a "duration" of 90th sec - that means it must be too slow, right?) which is the complete power up and down - not the hottest (most important part of the duration) moment of the fire. Don't worry - they'll work just fine.

The longer duration also allows for the complete shutter opening an closing - even at a high rate of speed you'll need all section to be even.

I know I'm missing something - lemme know if something still isn't clear. Good luck!
-Lew ;-)