Getting There
By Airplane
Located in the nothern edge of the city, Lisbon's Airport (Aeroporto da Portela) is the main international connection. As it is located quite close to city center, landings are usually quite nice - as airplanes descend over the city giving the traveller a unique vertical view.
Taxi to city center costs around 7€ + 1,5€ luggage fee. Buses 5,22, 44, 45 and 83 take you to several locations in and around the city. Aerobus 91 takes you up to Cais do Sodré where there is a connection to Cascais Estoril Coast Train (20 minutes).
By Train
There are 2 stations with international connections: Oriente Train Station (Estação do Oriente) and Santa Apolónia Station (Estação de Santa Apolónia). In fact they are in the same line and only 10 minutes of travel time apart.
There is a night train to Madrid every day.
Going to Paris by train requires a stop in Hendaye, in the french border with Spain. Then change to the TGV up to Paris.
International trains stop both in Oriente and Santa Apolónia Train Station. Oriente has a metro station, and is probably the best solution for backpackers heading to city center.
If you are going to Cascais Estoril Coast, you can get out in Oriente; take the red line of the metro to Alameda; then the green line to Cais do Sodré; from there you can get a train to several locations in the Cascais and Estoril Coast.
By Bus
In Sete Rios there is a bus national bus network node. You can get buses to almost every location in the country - http://www.rede-expressos.pt. From Oriente Train Station there are trains to the north line and to Algarve, in southern Portugal.