Public transport is good. There is now a direct rail link from the centre of Lisbon to Sintra via the Rossio tunnel. However the following are recommended as they are quicker from the airport:

Take a short BUS or TAXI ride from the airport to the nearest train stations, which are Roma and Areeiro. Sintra is the last stop on the line.  Other stations that have trains going to Sintra are Entrecampos, (take bus number 91 - find the Tourist Information Kiosk and leave by the nearest exit to it. The bus stop is on the right) and Jardim Zoologico/Sete Rios.