In either case you will have to go to Lisbon first.
From Faro Bus Station one can take a Renex bus to Lisbon Oriente Bus Station and then Metro to Cais de Sodre Station and then train to Cascais.
From Faro Bus Station one can take a Rede Expressos/EVA bus to Lisbon Sete Rios Bus Station and then Metro to Cais de Sodre Station and then train to Cascais.
From Faro Train Station one can take a Train to Lisbon Entrecampos Station and then Metro to Cais de Sodre Station and then train to Cascais.
The fastest public transport combination would probably require 4hrs30mins minimum each way.
For more info see Cubsur's excellent site: www.algarve-bus.info
