Aeroporto de Lisboa is 7km north of the city centre. The airport is served by buses 5, 22, 44, 45 and 83. The one-way fare on these buses is €1.40. A quicker, but more expensive alternative is the express Aerobus (route 91) and Aeroshuttle (route 96), which cost €3.50.
Buses depart from Terminal Arco do Cego, which is located on Avenida João Crisóstomo (metro Saldanha).
There are four main stations in Lisbon. The two stations most commonly used by backpackers are Estação Santa Apolónia, for trains to Porto and international services to Spain and France, and Estação Barreiro for trains to Évora and the Algarve. The other two stations - Cais do Sodré and Rossio - handle mostly suburban trains, although you may come here if you want to make a day trip to Sintra, Cascais or Estoril.
The A1 (also called the IP-1) is the main route for all traffic headed north. Your best bet is to take a train or metro to Oriente, then bus 5 towards the airport. Get off the bus when you get to Avenida Cidade do Porto and find a safe hitching spot on the northbound lane. This road becomes the A1 motorway shortly after this spot.
It is more difficult finding a ride south towards the Algarve or east to Évora and Spain as the motorways run through the centre and mostly carry local traffic until you're well out of the city.