The nearest station to Alvor is Portimão.
There are regular trains from Lisbon Gare Oriente and Entrecampos Stations to Portimão. You would have to change however in Tunes.
There are regular Renex Buses from Lisbon Gare Oriente to Alvor.
If you go to my blog at:
http://barlaventostravelblog.blogspot.com/
Scroll down on the right hand panel until you come to the section entitled:
»» Algarve & Portugal - Travel Transport Links
You will find links to the Renex Bus Timetables and Portuguese Railways - Lisbon/Faro and Algarve Lines Timetables.
Also have a look at Cubsur's site
http://www.algarvebus.info
You will find information there on local buses from Portimão to Alvor.
