By "operator" I take it you don't mean the lighting cameraman or DoP.
In most "single camera" cases the Op will know the DoP well and they'll have worked together many times so they'll have had quite a few chats and talks about the production, usually ending up with alcohol consumption. The operator will have been present prepping the gear and will know what the DoP is aiming for.
During the filming, the operator will often have more contact with the director than with the DoP unless there are problems like lights appearing in shot or lens flares which can't be cured with the matte box.
In television production (multi camera) the operators turn up on the day, have a walk-though rehearsal, a technical rehearsal and then a dress rehearsal before the show, in a ideal world. Often though one, or all, of the rehearsals don't happen and there's just a chat from the director, quick technical rehearsal (to check that everything works and that the cameras can physically get to where they're supposed to be) and then the show.
Having said that, every shoot, show and situation are different. There are no hard-and-fast rules.  | 
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