What's the cheapest way to get from Lisbon Airport to the city centre?

Metro is your best bet — take the Red Line from the airport directly to Alameda, then switch to the Green Line for most hostels in the centre. Runs until about 1am. Single ticket is €1.61 if you buy an Viva Viagem card (€0.50 deposit). Way cheaper than a taxi which will cost you €20-25. The Aerobus (€4) is also fine but slower during evening traffic.

Uber is actually pretty reliable from Lisbon airport and often only €12-15 late at night when there's no traffic. I used it after a late flight and it was door to door in 20 mins. Metro is great if you don't have big luggage.