Trenitalia operates a train from Trieste to Aquileia hourly. Tickets cost $3 - $9 and the journey takes 35 min. 2 other operators also service this route. Alternatively, APT Gorizia operates a bus from Trieste to Aquileia every 30 minutes. Tickets cost $6 - $7 and the journey takes 51 min. APT Gorizia also services this route hourly.
From Trieste Centrale train to Cervignano del Friuli - Stazione Ferroviaria then bus to Aquileia - Via Giulia Augusta Porte. 1 h 6 min 7€. From Trieste Autostazione bus to FVG Airport then bus to Aquileia Porte. 2 h 18 min 9€. From Trieste taxi to Aquileia. 46 min 236€. From Trieste drive to Aquileia. 46 min 7€.