How should quotes be integrated in an essay?

The smoothest and most preferable way to integrate quotes in your essay is to incorporate the quote into the flow of your sentence, so that the quote fits seamlessly between your words. 

For example, if I wanted to discuss the beginning of Hamlet's famous soliloquy (Act 3 Scene 1):

To be, or not to be, that is the question:Whether 'tis nobler in the mind to sufferThe slings and arrows of outrageous fortune,Or...

The smoothest and most preferable way to integrate quotes in your essay is to incorporate the quote into the flow of your sentence, so that the quote fits seamlessly between your words. 

For example, if I wanted to discuss the beginning of Hamlet's famous soliloquy (Act 3 Scene 1):

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,
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 heart-ache and the thousand natural shocks
That flesh is heir to: 'tis a consummation
Devoutly to be wish'd.

I could do so in the following way:

Hamlet is at a point of crisis here, as he asks himself whether it is better to exist, and suffer "the slings and arrows of outrageous fortune", or whether it is better to refuse this suffering by choosing to die. The way Hamlet sees it, to choose death is to "end/The heart-ache and the thousand natural shocks/That flesh is heir to"; or in other words, death is a means of escaping life's troubles.

As you can see, the quotations from the play flow seamlessly with my own words. However, this can often be quite difficult and time-consuming to do well. It is also perfectly acceptable to occasionally include quotations in parenthesis where you require them as evidence, as in the following: 

Hamlet is clearly grappling with ideas about death and suffering in this soliloquy. Hamlet seems to believe that life is a great struggle, and that fate makes life a series of hurtful blows ("The slings and arrows of outrageous fortune") and unending difficulty ("a sea of troubles"). 

The second example does not flow quite as nicely as the first, but it is not jarring or awkward. If you are having trouble integrating a quote into the body of your sentence, it can be okay to include it in parentheses where it is needed.