The Rasht airport (☎ +981333727001-3) is serviced by domestic Iran Airlines (Iran Air, Taban, Kish, Aseman, Caspian, Aseman, Zagros and Naft).
Direct domestic flights are available to Tehran, Shiraz, Mashhad, Kish, Ahwaz, Asalouyeh, and Bandar Abbas. Direct international flights is available to Istanbul, Turkey. From the airport, you can take a taxi to to Rasht city center. 8km of the city center (~20 minutes).
Like everywhere in Iran Rasht is well connected with Tehran and neighboring towns by bus. You can use the Azadi Terminal (Tehran West Bus Terminal) to take Bus (~15 USD) or Taxi to Rasht. From Tehran to Rasht 350km North of the Tehran (~4 Hours). A private taxi also is very cheap, about 40 USD.