What responsibilities in Theatre do to following roles have?

Question:Lighting Designer/Operators.
Sound Designer/Operators.
Stage Hand's.
Stage Manager's.

Best Answer - Chosen by Asker: Lighting Designer/Operators.
Sound Designer/Operators.
Stage Hand's.
Stage Manager's.

First of all, all these people work co-operatively with the director.

The lighting designer decides in consultation with the director, what the lighting will look like. It might be interior lighting in act 1, exterior early morning in winter in act 2, and exterior sunset in act 3. He/she will arrange for the lights to be set up in such a way that those effects ca be achieved. The lighting operator will work the lights during the performance so that those effects happen at the right time.

The sound designer is responsible for planning and arranging everything you hear during the performance. This could be very simple, in a small studio theatre with no microphones, it might just be playing some music while the audience assembled, playing a telephone ringing in act 1, some birdsong in act 2 and a car arriving in act 3. It could be very complex, co-ordinating microphone/amplification for spoken voice and for singing for a large cast with the orchestral music and sound effects for a big musical, like 'The Lion King'.

Stage hands work under the direction of the stage manager, building sets, moving scenery etc.
The stage manager is responsible for seeing that sets are built, furniture and props are placed correctly, and scene changes happen as needed. He/she may mark the stage with tape to indicate the positions of the furniture.
During the rehearsal period and later during the performances, he/she will let the actors know when they are needed for rehearsals, when their next performance is etc.
He/she is also responsible for obtaining and organising props. There will be a props table backstage, where all the props are kept in labelled spaces, and the actors collect their props from the table and return them their afterwards.
The stage manager often calls the actors to the stage when they are needed during the performance, and gives standby cues and 'go' cues to the sound and lighting operators.

I hope I've remembered everything, andI hope this helps.