The main difficulty of staging the famous "to be or not to be" soliloquy in William Shakespeare's Hamlet Act 3 Scene 1 lies in its very fame. Audiences expect and know the speech, and often use it as a way of judging the quality of the acting in the play.
There are two approaches you can take. If you have a spectacularly good actor such as Sir Laurence Olivier, you do not want to do anything to detract from his performance. Thus dimming all the other lights and having a single follow spot on him will give the audience the best opportunity to watch spectacular acting with no distractions.
If an amateur or student actor is attempting the same speech, the staging that would highlight the brilliance of a superb actor will show the flaws of a weak one. Thus you might use more atmospheric staging. Take a cue from the lines:
To die, to sleep—
No more—and by a sleep to say we end
The heartache, and the thousand natural shocks
That flesh is heir to. 'tis a consummation(70)
Devoutly to be wish'd ...
Use some sort of dreamscape for the staging (dry ice smoke, shifting patterns of coloured light, perhaps gauzy fabrics in a wind machine with the Hamlet moving in and out of shadows), and have elaborate blocking and movement to break up the speech and add emphasis so that not everything depends on sheer vocal skill.