The first words that the titular character speaks in Shakespeare's Hamlet are spoken as an aside (a character's thoughts spoken aloud), which the audience hears but the other characters on stage do not hear. In Shakespeare's plays, characters speak the truth in asides and soliloquies for the simple reason that they're speaking to themselves and therefore there's no reason to lie.

With Hamlet's first words, "A little more than kin, and less than kind" (1.2.67), Shakespeare takes the audience directly into Hamlet's confidence and into his life. Shakespeare puts Hamlet in the forefront of the audience's collective mind. From that moment, Hamlet is the primary focus of the audience's attention. Everything that occurs in the play is seen through Hamlet's eyes and is filtered through what the audience believes are Hamlet's sensibilities. It's truly remarkable that Shakespeare accomplishes all of that with a single line of iambic pentameter.

It's important to look at Hamlet's first line in the context in which it occurs and as the first and only words that the audience has heard Hamlet speak so far (not in hindsight, with knowledge of the entire play).

At this point in the play, the audience knows nothing about Hamlet's scene with the Ghost ("O my prophetic soul! "), or Ophelia ("Get thee to a nunnery"), or the Players "Speak the speech"), or Hamlet's duel with Laertes ("A hit, a very palpable hit"), or Hamlet's last line: "The rest is silence."

The audience hasn't yet heard any of Hamlet's soliloquies, in which he exposes and explores his innermost thoughts and through which the audience learns more and more about him. The audience hasn't even heard Hamlet's pun in his next line about being "too much i' the sun" (1.2.69).

The only words that the audience has heard Hamlet speak so far are "A little more than kin, and less than kind," in response to a line from Claudius.

CLAUDIUS: ... But now, my cousin Hamlet, and my son (1.2.66)

Considering that the audience knows almost nothing about Hamlet (his name has been spoken only once thus far in the play, in the preceding scene, and this is the first time he appears on stage), this first line needs to be taken purely at face value. In fact, someone in the audience who has never seen or read Hamlet and knows nothing about the play might not even know which of the characters on stage is Hamlet until Claudius addresses him:

A little more than kin

First of all, who is "a little more than kin"? To whom is Hamlet referring? Claudius, himself, or both? In what way(s) is Claudius, or Hamlet, or both "a little more than kin"? Do Hamlet and Claudius have more than a kinship relationship?

Claudius addresses Hamlet as "my cousin" and "my son." It might be unclear to some members of the audience what the relationship actually is between Claudius and Hamlet. Is Hamlet Claudius's cousin? His son? If not, why does he call him "my cousin" or "my son"?

and less than kind.

Again, who is "less than kind"? "Less than kind" in what way(s)? "Less than kind" in terms of actual kindness towards one another? In terms of "he's not my kind"? In terms of "we're not at all alike"? Or all the above?

All the audience knows about Hamlet from his first line is that they still don't know much about him, except that he can turn a clever phrase, even though the meaning of the phrase is wholly unclear.

Essentially, the audience knows very little more about Hamlet after he speaks his first line than before he spoke his first line.

The audience simply needs more information, but thanks to Shakespeare's skill as a playwright, the audience is immediately drawn to this enigmatic character and into his life, and the audience is going to spend the next four hours watching the play to find out as much as they can about him.

Hamlet's first words appear in Act 1.2, line 65.  The line is:

A little more than kin, and less than kind.

Delivered as an aside, or spoken directly to and only to the audience, the line uses puns to ridicule Claudius, who has just referred to Hamlet as his kinsman (cousin) and his son.  Kinsman is used for relatives outside of one's immediate family, and son, is of course, son.

Hamlet plays on these two terms in his response. 

When Hamlet says that Claudius is more than kin, he is saying that Claudius is too much of a relative, both uncle and stepfather:  the stepfather part is too much.

When Hamlet says that Claudius is less than kind, he is saying the following:

• Claudius is unkind for taking the throne from Hamlet, the former king's son and rightful heir.
• Claudius is unkind, of a certain kind, an unnatural kind, because he has married the wife of a dead brother, which is considered incest in Shakespeare's time and within the play.

Hamlet is sharp, witty, and definitely unhappy about his uncle's marrying his mother and claiming the Danish throne.  Hamlet doesn't yet suspect Claudius of murder, since this scene appears before Hamlet's meeting with the Ghost.  But he certainly does not consider himself to be the new king's son. 

In addition to the superb answer above, the first line is a paradox, verbal irony, and an equivocation, all of which reveal opposites conjoined.  The phrase "A little more than kin and less than kind" shows Hamlet's wit and the duality of his nature.

Hamlet will reflect dualities in his words and character throughout the play, namely in his monologues and soliloquies, the most famous of which is "To be or not to be."  Most of these paradoxes show the split in modern man, as he is split between action and observation, will and reason, freedom and authority, consciousness and narcissism. All of these paradoxes add up to man's existential questioning of a God (Hamlet's father, the Ghost) whose responses may or may not be his own, a kind of single-minded double argument.

Hamlet's first line is an aside:

"A little more than kin and less than kind" which suggest all kinds of things, given that he is responding to his uncle Claudius' referring to Hamlet as his son.  Hamlet is likely bringing up the idea that he already suspects his uncle is a devious man and certainly not just playing the role of uncle and father, now that he has married Gertrude, Hamlet's mother.  He is the king, he is perhaps a murderer, all kinds of fun implications in Hamlet's words.

His second line is:

"Not so, my lord; I am too much i'the sun."

He is letting us know that he is not actually oppressed by gloominess but is in fact much too exposed, he'd rather not have to grieve in public but since everyone else has moved on, he is forced to be the only one still grieving for his father.