Using public transports
Use the bus service nº91 from Carris, that goes from the airport to the CP Cais do Sodré train station. In this station you will have access to the Cascais line that serves the Estoril Coast. Departures happen every 20 minutes, from 6 AM until 1 AM.
Without leaving the airport you can reach by Metro the Cais do Sodré station and from there, take the train to Estoril and Cascais. In Alameda station must spill for the Green Line to get to Cais do Sodré, from where the train that makes the whole Atlantic coast from Lisbon to Cascais leaves, or go out in Rossio station if you want to visit the mystical Sintra.
Taxi:
You may also pot for the Taxi. Seek, just outside of the Lisbon Airport, one of the many Taxis available to take you to your destiny – Estoril Coast.