Aerobus: (line 91) links the airport to the city center. It departs every 20 minutes 7AM-9PM. Aeroshuttle (line 96) links the airport to the city centre via the Sete Rios bus station and the Financial district. Tickets on both cost ?3.50 and are valid on all public transportation lines, such as buses and surface trams (but not for metro) for one day. Or take the bus 745 fom Airport to city center for only 1.45
Bus: lines 5, 8, 22, 44, 45, 83. Board fare is 1.45. 7 Colinas transport card, can be used which can be bought at the airport post office. Note that you are not allowed to take suitcases on these buses.
Taxis: cost about 10.00 from the airport to the city center. Charge is according to the meter, adding ?1.20 per item of luggage. As with many cities, watch out for dishonesty and if you think you are being charged significantly more (paying ?45 to get into the city but only 6 back to the airport is not unheard of) ask for their number and a receipt, and make it clear you plan to complain. Any policeman should take care of the situation if there are signs of fraud. Lisbon people, in general, really hate dishonest taxi drivers, so, it will be easy to get a hand in case of a conflict. To avoid fraud, you can buy a taxi-voucher in the airport, which is good to go anywhere in the center, with luggage. Make sure to ask the driver how much he estimates the fare will be before getting in the taxi, which will diminish the chance for a surprise bounce in the price. If you want to take a taxi, go to the departures area (and never! to the arrivals area), it's more likely to get an honest driver there. Make sure the driver starts the meter when the journey starts.