Quinta da Marinha resort is located on the Atlantic side of Cascais, the famous coastal town about 25km from Lisbon.
There are no direct buses or trains. You could organise a private transfer or taxi as suggested above.
Another transfer company is: http://bit.ly/alg5sn
Alternatively, you could get the Aerobus service from outside Lisbon Airport arrivals hall to Cais de Sodre station:
See: http://bit.ly/9b2Ga3
From Cais de Sodre Station, you would then have to get a train to Cascais which takes about 35 minutes, depending on time of day/week/night.
On weekdays, trains that leave every 15 minutes on the 15 minute mark are high speed to Cascais.
Outside Cascais Station, you should be able to get a taxi for the 3km 5/10 min ride to Quinta da Marinha.
