It might seem strange, but the Lisbon taxi service is not expensive at all. I choose it to reach the center form the aeroport. is about 10 km and it will cost me €12.35
You can calculate the amount for your travels here
Alternatively you can move with the subway, with 4 lines really arrives everywhere and the ticket costs just € 1.45
The underground station is integrated into Terminal 1, easier than that!
To use the subway, bus or tram you must first purchase the Viva-Viagem card for € 0.50 and then load it. It can be bought and loaded directly on the subway at the vending machines or at authorized stores (almost all tobacconists and newsstand)
You will find all the informations here
On the website ther’s also a “travel plan” very useful to know what line to take and the price of the route.
Alternatively, you can buy a day ticket for € 6.15 or the Lisboa Card (24, 48 or 72 hours) that allows you to save on transport but also on attractions and tours