In arcade mode and time attack mode(TAM) you have to beat their time and be the first in ranking. In scenario mode(SM) you have to clear the series by using them.

Car	How to unlock
964_BB	Series 12 in SM
BCNR33_KUROKI	Series 6 in SM
BCNR33_MOTOKI	Course 10 in TAM
BCNR33_SONODA	Course 4 in TAM
BCNR33_TEDUKA	Course 9 in TAM
BCNR33_YAMAMOTO	Course 6 in TAM
BCNR33_YAMANAKA	Series 4 in SM
BNR32_HIRAMOTO	Series 2 in SM
BNR32_REINA	Series 1 in SM
BNR32_TOMOYA	Series 10 in SM
BNR34_GOTO	Course 5 in TAM
CP9A_EIJI	Series 7 in SM
CP9A_MAKI	Course 3 in TAM
FC3S_KIJIMA	Series 9 in SM
FD3S_MASAKI	Series 3 in SM
FD3S_OHTA	Course 1 in TAM
FD3S_OKI	Series 8 in SM
HGZ31_HARADA	Course 2 in TAM
JZA80_KEI	Series 5 in SM
S30_AKIO	Arcade mode
UCF11_GACHAN	Course 8 in TAM
Z32_MAKOTO	Series 11 in SM
Z32_YAMASHITA	Course 7 im TAM