There are two big train stations in Lisbon: Santa Apolónia and Gare do Oriente. However, if you are entering Lisbon from the south, you may want to get off at Entrecampos or Sete Rios: their metro stations are a few stops closer to the central and old town.
If arriving from the north (Porto, Gaia) and center (Aveiro, Coimbra) of Portugal use Santa Apolonia, close to Alfama/city centre.
Cais do Sodré is another important train station, connecting Lisbon to Cascais/Estoril coast.
There are fast links with speeds well over 200 km/h from Lisbon to the Algarve and from Lisbon to northern cities such as Porto, Braga, Guimarães, Coimbra and Aveiro, but on most routes there are intercity services which still are fast enough and a good alternative to buses or cars. From Lisbon, there are also frequent links to Cascais and Sintra, popular traveller routes.