1. The first difference that you notice is the setting. The classical version takes place in Verona, a city in the north of Italy and the movie also takes place in Verona, but in this case is Verona Beach, a modern city in USA. Also, the century is different, because the book takes place in the XVI century and the XX century (the movie was made in 1996).
2. All these things are opposites, just like Romeo and Juliet. They belong to different families which are confronted, that's why they are like the day and the night or the water and the fire, they shouldn't be together.
A part from that, the water and the fire have another meaning: the water represents the love and the fire represents the hate between the two families. We can see water during all the movie for example when Romeo and Juliet first meet, they see each other through a fish tank, representing the love at first sight, or after the party, Romeo and Juliet are both in the swimming pool, which represents that they have fallen in love. The fact that the water appears during all the movie means that the love is always there.
We can see fire at the beginning, in the petrol station, in which there is a fight between the Montagues and the Capulets.
These two elements have these meanings representing that love can make hate disappear, for example Romeo and Juliet, who should hate each other, but for them love is stronger than hate, just as the water is stronger than the fire because is the one who can put it out.
3. In the book all the characters speak in verse, but the ones you notice the most are Romeo and Juliet, because they are the ones who speak the most and who speak the most about love. In the movie the majority of the characters speak in prose, except Romeo, Juliet and maybe a few more who sometimes speak in verse.
The narrator in both, the book and the movie, is an omniscent narrator, who's not any of the characters of the story. In the movie, it is the news reporter, who explains the Romeo and Juliet story.
5. Lots of things change from the book: the swords are guns; the style of the clothes is so much different and actual; the Capulets' party is also different (the music, Mercutio's perfomence, which isn't in the book, the house were it is celebrated, etc.); the houses in general are much more modern; the things happen in the city and in the beach, while in the book they happen in the middle of a ancient town or in the forest; the carriages and horses are fancy cars; the Prince of Verona is a policeman, etc.

