In Lisbon city you may go almost anywhere by subway. Subway to Parque das Nações, down town, Railway stations, etc. Suburban trains to Estoril coast line, Cascais and Sintra.Buses to some points of Lisbon. Metro costs 0.55 Euros, trains to Sintra and to Cascais around 2. You may get a tourist pass in any Carris ( bus Lisbon Company) or Metro Station. There is also group tickets for suburban trains ( CP ). Taxis just take 4 persons. If you get a train to Sintra, to visit Sintra you may and you should do it on foot. There is also bus tours to Cabo da Roca, the end of Sintra mountain and the most western point of Europe. To get there tours left from Lisbon. But you also may rent a car. It's not expensive and gas is around 1 Euro/ Lt. From airport you may take the Airport bus to downtown.
One of the best ways to travel around Lisbon is by Metro. It's really nice. Some stops has openair stations. But most of them are under earth. In Lisbon metro and Portugal is cheaper than in Spain so...better for your economy!
The best way to get arround is by train, metro and bus.
I got a Lisboa Ticket for 2 days (it is available for 1-4 days) which includet most busses and the metro and also the complete entrance fee for some places like museum or a reduced price for other places.
A nice way to get arround also to Belem is by Tramway as you can see on this picture.
The visitors pass is a Must at only 14 euros for 7 days. You can travel on the metro, the bus and the trams for as many trips as you like. This pass can be purchased at any metro station.
This is the train station you should go out if you want to go to the city center, Av. da Liberdade and Parque Eduardo VII.
More information about the Metropolitan Lisbon is available on their site.
metropolitano de lisboa