In Shakespeare's time, stage production was far more limited than it is today. We often see his plays produced in theaters with curtains and backdrops, where the actors are distinctly separated from the audience. His plays would not have looked like that. Often the plays took place outdoors, in innyards, as often as they did in theaters, and the theater itself was sometimes open to the elements. The setting would feature a mostly bare stage with props carried on and off, and no clean breaks between scenes. The visuals of the setting were left to the audience's imagination. The dialogue and acting took precedence, and the action was indicated by certain characters' speeches. For instance, in Hamlet, we know the opening scene takes place on a watchtower from the action of the sentinels.
In the same way, Shakespeare's imagery is evocative throught he dialogue rather than through explicit stage instructions, leaving modern directors free to come up with interesting and unique ways to set the mood. The imagery that most sets up that climate of fear and despair in Hamlet comes from the plot and from Hamlet's soliloquies, in which he epitomizes confusion and despair himself. The presence of the ghost of his father and the fact that he knows his uncle killed his father and that he plans to kill Claudius in return also add to the suspense.
The imagery is thus created through the combined vision of the playwright, the actors, and the director.