The quickest and most efficient way to reach Porto's city centre from the airport is by metro – line E-Violet (Aeroporto – Trindade). This line operates daily from 06:00 – 01:00 and from here, getting to the city centre takes about 30 minutes. The Andante ticket (which has a price of 0.60€) needed for this journey can be purchased at any of the automatic ticket machines in the Metro station – occasional ticket (Z4). It costs 2€, is valid for 1 hour and 15 minutes and is also rechargeable. Don't forget, one card per person.
To get to the city centre by bus, you can take either line 601, 602 or 3M (12:30am-5:30am). In this case, you can buy a single trip ticket on the bus, costing 2€.
Another option is to take a taxi which costs between 20€/25€ or rent a car at the airport.