Who said it, to whom, and what is he/she talking about?" ... The dread of something after death ... Makes us rather bear those ills we have, Than fly to others that we know not of."

This speech was made by Hamlet in a soliloquy, that is he was talking to himself (thinking out loud). The speech was a ruse however, and was actually directed at the people he knew were spying on him, so that they'll continue to believe his pretended madness.

Explanation:

This speech is the famous "To be or not to be" that Hamlet made contemplating death after his discovery of what happened to his father.

He was contemplating the uncertainty of life after death, and whether he should stick to what he knows (life), rather than choose the other alternative to find himself in an existence he knows nothing about.

However hamlet knew he had an audience listening behind the drape, so the speech was directed at the them.

Hamlet was plotting and playing politics, he was trying to throw them off his trail by feigning madness to avoid detection of his main objective, that is to have the truth be told.