Cascais is a suburb of Lisbon situated about 20km along the River Tejo estuary from Lisbon centre.
From Madrid you will have to get to Lisbon centre first and then by train to Cascais.
Even by air it will be difficult to do in a day as getting from Lisbon Airport to Cascais by public transport will take at least two hours.
Low Cost Airlines Easyjet.com and Vueling.com operate Madrid to Lisbon and vice versa several times per day.
Easyjet have a weekday departure from Madrid at 06:55, arriving Lisbon at 07:15. (Portuguese Time.)
Vueling have a weekday departure from Madrid at 09:45, arriving Lisbon at 09:55. (Portuguese Time.)
You would then have to get the Aerobus service from outside the arrivals hall to Cais de Sodre:
See: http://www.carris.pt/pt/ficha-de-carreira/91/descendente/
From Cais de Sodre you would them have to get a train to Cascais which takes about 35 minutes. On weekdays, trains
that leave every 15 minutes on the 15 minute mark are high speed to Cascais.
Easyjet has a return flight daily from Lisbon to Madrid leaving at 20:25, arriving 22:40.
Vueling has a return flight daily from Lisbon to Madrid leaving at 20:45, arriving 22:55.
There is only one overnight train per day between Lisbon and Madrid and buses take 6 to 7 hours. I strongly recommend flying.
