on airport take a bus to Cais do Sodré: 91 (Aerobus, €3,50, around 25 min) or 44 (€1,50 on-board fare, around 45 min) or 208 (dawn service, €1,50, on-board fare). See detailed information on Carris site
on Cais do Sodré (station) take a train to Carcavelos (station), €1,80, around 26min. See detailed information on CP Cascais line