how to do lisbon: use the metro
The Lisbon metro is modern, efficient, and pretty easy to use. The only hiccup I experienced was when I first arrived at the airport and couldn't figure which direction to head in.
waiting on the Comboios suburban train from Belem to the city center
The metro goes to all of the neighborhoods and points of interest in central Lisbon. A reloadable, multi-trip card can be purchased and refilled at machines in every station. One of the best things about Lisbon's public transportation system is that you can use the same multi-trip card on the underground metro, above-ground trams, trolleys and buses, and the suburban trains that go all the way to Cascais and Sintra.
For long-distance destinations like Coimbra and Porto, you'll have to purchase a separate ticket for one of the regional or inter-regional trains that depart from Santa Apolonia Station.