You first have to meet people by driving around the city and not really beating them, but hanging with them for a certain amount of time. Whether or not you hang with them well is indicated by the color of the arrow above the other car. After you hang with them for a while, you will be given thier phone number. Calling this number will open up actual races for you to drive in. You must take first in these races to advance. Eventually, you will get everyone's phone number, clean them out of pink slips and race the final opponent. London is opened for you after New York is completed in this manner.
Hope this helps. Its a good game, especially for a first gen PS2 title, but it loses depth after a time. The only reason I'll still play is to play "tag" between myself and another player's car. BAM!