I'm living in Nice and I'm studying near the airport so I might be able to help you...
To get to the train station from Terminal 1 or 2, you have three options: a taxi (extremly expensive !), bus line 99 or bus line 23.
Bus line 99 is called "direct aéroport", it runs directly from Nice station to Nice airport and there are only a few stops between the two. The journey takes approximately 15 to 20 mn. The dark side: this bus is a rip-off ! You have to buy a 4€ all day pass to use it...This bus leaves from platform 1 at T1, and platform 4 at T2.
Cheapest option: take bus 23 direction "St Maurice" ! It stops at Nice station, but it's way slower than line 99. The journey takes between 30 and 45mn and a one way ticket costs 1€30. Beware: this bus doesn't run throught terminal 2. If you arrive at terminal 2: take the free shuttle bus (very frequent and convenient) to terminal one and then board bus 23 at platform 6.
Don't hesitate if you have more questions !
[Edited 2007-02-06 19:20:38]