The nearest airport to Gangtok is at Pakyong. But flights to Pakyong are not yet regular. Bagdogra is the next nearest one. From Bagdogra, you will get private cars to Gangtok.  If you are looking for shared transport, then you have to come to Siliguri SNT stand from where you will get buses and shared sumos to Gangtok. The nearest Railway station is New Jalpaiguri. You will get both private and shared vehicle from NJP or Siliguri to Gangtok.