Tybalt's FIRST words in the play are:

What, art thou drawn among these heartless hinds?
Turn thee, Benvolio, look upon thy death.

Tybalt's first reaction to problems is to fight.  He is not a talker.  He thinks first of settling issues with violence and aggression. 

He then says to Benvolio who is trying to avoid violence: "What, drawn, and talk of peace! I hate the word"  He is not a person who sees opportunities for peaceful resolution.  

Benvolio later calls him "The fiery Tybalt, with his sword prepared," when he explains what happened in the violent encounter.  Tybalt always seems to have "his swrod prepared."

Later, when Tybalt recognizes Romeo's voice at the party, his first thought is "Fetch me my rapier, boy." and "To strike him head, I hold it not a sin."   This, of course, foreshadows what later will happen when Tybalt attempts to kill Romeo and gets killed instead.   

1. As the foil of the Petrarchan lover Romeo who bemoans the loss of his love, Rosaline, wandering behind the first scene, and later pursues Juliet, the bellicose Tybalt launches himself as an aggressor in Scene 5 of Act I:

This by his voice, should be a Montague
Fetch me my rapier, boy. What dares the slave
Come hither, covered with an antic face,
To flee and scorn at our solemnity?
Now, by the stock and honor of my kin,
To strike him dead I hold it not a sin. (1.5.56-61)

2. Then, in Act III, Tybalt finds the opportunity to accost his foes in the form of Romeo's friend Mercutio, whom he challenges, "Mercutio, thou consor'st with Romeo--(3.1.44) Then, when Romeo appears and tries to ameliorate the situation, stating that now he loves Tybalt, Tybalt declares his animosity, 

Romeo, the hate I bear thee can afford
No better term than this--thou art a villain (3.1.59-60)

3. Romeo denies being his enemy since he is now married to Juliet, but Tybalt rejects him and challenges him to fight,

Boy, this shall not excuse the injuries
That thou hast done me, therfore turn and draw (3.55-56)

4. Romeo argues that he has never injured Tybalt, instead stating that he loves Tybalt. Incensed, Tybalt declares that Romeo's affection does not excuse the previous injuries, This conversation between Romeo and Tybalt  does nothing but incite Mercutio, who calls Tybalt a "[G]ood King of Cats." and challenges him to a duel, to which Tybalt replies, "I am for you," (3.1.81) and they fight until Mercutio is mortally wounded.

5.After Mercutio is gravely injured, Tybalt returns and Benvolio tells Romeo, "Here comes the furious Tybalt back again" (3.1. bent upon dueling Romeo and promising to kill Romeo and send him where the slain Mercutio has gone.

Thou, wretched boy, that didst consort him here.
Shalt with him hence. (3.1.131-132)

But, as he fights, Tybalt is slain by Romeo. As a result of his death, Romeo must flee Verona and hide in Mantua.