The cheapest way to get from Lisbon airport to the centre is by bus. If you’re travelling light, get on a regular route which passes all the major avenues. The No. 44, 45 or 83 Carris buses cost about €1.50, or even less with a 7 Colinas (internal link) card.
If you have a lot of bags, you’re better off getting the AeroBus 91. This still only costs about €3.50, and runs from about 08.00 to 20.45.
If you arrive in the middle of the night, get the Carris 208 night bus. Or you could splash out on a taxi. This is the fastest way to reach the city centre. It’s better to pick one up outside departures, as opposed to arrivals, to avoid rip-offs. And it shouldn’t cost you more than €15-20 Euros, even with heavy luggage.