How do you earn money after you have completed the game?

You can't. You've completed the game so there is nothing to earn money for.
There is a cheat code for earning more money but I don't remember it and I don't know if it works when you have completed the game

Go to the world map and race any of those races (even the ones that have been completed). When the race starts, press start and go to restart. Then when you win the race, you should get paid..

You can actually do this anytime you are in freeroam including after the game and in quick race mode, at your map or mini map, there should be orange triangles (other ai racers) driving around what you're going to want to do is follow them, if you follow closely enough to these ai cars the race icon should appear above the Cingular logo as it does when you are parked in a marked race on the map, press enter to begin. These orange triangle ai are outrun racers, the idea here is to race as far ahead of the opponent as quickly as possible. Outrun races take place on the open city map and thus you can race any roads unlocked in career mode(in your case the entire city). Despite being on an open map I specifically say to race ahead because these races are cat and mouse, you're pretty much asking to lose if you dart in any random direction. Additionally Outrun races in Career mode are bet races; if you win you get a hundred, if you lose you lose a hundred. These outrun races are also available in freeroam under quick race in the main menu so you can try them there no risks without losing your hard earned career money. Referencing what I said above about availability, you can actually perform outrun races as soon as you have Rachel's car, this can help on a new career play.