Act 1, like most first acts in drama, is mainly about setting the scene, and introducing the characters. It largely builds toward the Capulet party in its final scene: Act 1, Scene 5.
The first scene is a largely comic scene, introducing two yobbish Capulets, whose banter escalates into a street brawl. The Capulet and Montague feud has been going on for a long time, and is still pursued with enthusiasm by both families.
Next we meet Paris, whom Capulet is inviting to a party that evening. He - who we meet in detail before we meet Juliet or Romeo - is a likely suitor to marry her.
Romeo and Benvolio, two young Montagues, are introduced next. We learn that Romeo is in love with Rosaline, who doesn't return his advantages. And Benvolio says he will drag Romeo to the party, in order to get his mind off her.
Next (Act 1, Scene 3) comes the first of many interior Capulet scenes centred around Juliet. We meet the nurse, and Lady Capulet, who are keen to know whether Juliet wants to marry Paris. Again, she says she'll meet him at the party that night, and see what she thinks.
Act 1, Scene 4 introduces us to Mercutio, as the Montague boys get ready to crash the Capulet party. Mercutio and Romeo have an argument, during which Mercutio improvises his Queen Mab speech. Benvolio calms them down and they all go to the party.
Act 1, Scene 5 is the party. Romeo and Juliet speak and fall in love. Tybalt hears Romeo's voice and swears revenge.