Most flights arrive at Melbourne Tullamarine Airport, about 25 minutes northwest of the city centre. The SkyBus express shuttle runs frequently to Southern Cross Station. A taxi or rideshare to the CBD costs around AUD 60-70. There is no train connection to the airport.
Some budget carriers, including some Jetstar services, use Avalon Airport near Geelong, about an hour southwest. Check which airport your flight uses before booking ground transport. V/Line trains connect Melbourne to regional Victoria from Southern Cross Station, and interstate trains and buses also depart from there.