Assuming one arrives at Lisbon Airport between 07:00 and 20:30, it is usually preferable to avoid the Metro and having to change lines and get the Yellow Bus AeroBus Line 1 from Lisbon Airport which goes directly to Cais de Sodre Station:
Tickets currently cost € 3.15
One can then catch one of the trains to Cascais that leave +- ever 15 to 20 minutes or so. Prices are currently € 2.15 one way.
Timetables (in Portuguese here):
Cascais is the terminus for the "Linha da Cascais".
Taxis are available outside the station and it is recommended taking taxis to Hotels if one has bags as most hotels are a little distant from the station.
Buses also leave from just outside the station. Timetables for Scotturb services from Cascais Station and other locations can be found here: http://bit.ly/1afj2Fw
After 2130, for security reasons on the linha da Cascais, an airport transfer from Lisbon Airport to Cascais might be more advisable.