For an extended summary of the first act, see the enote on Romeo and Juliet.
Here's a medium length summary:
The prologue tells the audience that the Montagues and the Capulets have been fueding for hundreds of years.
The first scene gives an example of this, with a quick M/C clash. Tybalt challenges Benvolio to a duel, but the Prince breaks it up. Romeo is introduced, and we find out that he's in love with Rosaline.
The second scene follows the Capulets, and introduces two key facts about Juliet: she's only 13, and Paris wants to marry her. A servant is supposed to invite people to a party thrown by the Capulets, but can't read the invite list; when Romeo and Benvolio read the list, they find out Rosaline will be there, and plan to go.
In the third scene, Juliet is counseled to get ready for marriage.
In the fourth, Romeo and friends head for the ball. Romeo's friends tease him about being so hot for Rosaline; Romeo has a bad feeling about the ball, but goes anyway.
The fifth scene is in the Capulet's house. Romeo sees Juliet and falls immediately in love. Tybalt recognizes him as a Montague and wants to kill him.
And here's a short summary:
The Montagues and Capulets are sworn enemies. Romeo is a Montague. Juliet is a Capulet. He's in love with someone else, and her family wants to Juliet to marry someone else, but when they meet at a party, they fall instantly in love.