There is a bus from the train station that runs, in this order, to the town [and the National Palace], the Castelo dos Mouros, Pena Palace, the town, and back to the station. You can get a rover ticket which allows you to get on and off at will.

Alternatively you can buy a more expensive rover which allows you to use local buses to the beaches and to Cascais as well. It is probably not worth it for less than two journeys.