In order to figure out how to perform this soliloquy correctly, you must first think about its underlying meanings.

To be, or not to be, that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune(65)
Or to take arms against a sea of troubles,
And by opposing end them. 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.

Hamlet is here considering death, whether or not he should continue "to be." Is it really more honorable to face all the punishments of life than it would be to simply fall asleep in death?

To die, to sleep—
To sleep—perchance to dream. Ay, there's the rub!
For in that sleep of death what dreams may come,
When we have shuffled off this mortal coil,
Must give us pause—there's the respect(75)
That makes calamity of so long life.

Here, Hamlet begins to wonder "what dreams" (or rather, nightmares) the afterlife would bring him if he were to prematurely end his life.

For who would bear the whips and scorns of time,
The oppressor's wrong, the proud man's contumely,
The pangs of disprized love, the law's delay,
The insolence of office, and the spurns(80)
That patient merit of the unworthy takes,
When he himself might his quietus make
With a bare bodkin? Who would fardels bear,
To grunt and sweat under a weary life,
But that the dread of something after death(85)
The undiscover'd country, from whose bourn
No traveller returns, puzzles the will,
And makes us rather bear those ills we have
Than fly to others that we know not of?

Hamlet here acknowledges that life offers a lot of discouragement, and it would be much easier to make one's "quietus," or relieve oneself of these burdens, "with a bare bodkin," or a mere dagger. The only problem with this, as Hamlet sees it, is the chance that the act of suicide would deliver him to other, perhaps far worse, torments.

Thus conscience does make cowards of us all,(90)
And thus the native hue of resolution
Is sicklied o'er with the pale cast of thought,
And enterprises of great pitch and moment
With this regard their currents turn awry
And lose the name of action. Soft you now!(95)
The fair Ophelia! Nymph, in thy orisons
Be all my sins remembered.

Despite his desire for escape, Hamlet's fear of the beyond forces him to continue living. He concludes with a glimpse of Ophelia, partly the source of his troubles, whom he has just seen.

Any performance of this soliloquy should portray realistically the emotions of fear and exhaustion that fuel Hamlet's conflict in this scene.