Shakespeare's plays were performed in a theatre. For more complete information concerning these theatres, please see the link below.
Quite simply, the stage thrust out into the pit. Since there was no electricity, natural light was necessary so the center of the theatre was open to the sky and if it rained, those in the pit got wet.
The stage had three levels and several entrances.
Plays were performed with no scenery but props and furniture were important. For example thrones and swords would be used.
They were performed with actors wearing contemporary costumes.
What was important to the Elizabethan audiences was the story.
Please see the link below for more answers.