Travel from Porto Airport to Porto City Center There are two easy ways to go from the airport to the city center and to the 2 main train stations in Porto (Porto-São Bento / Porto-Campanhã):
By metro: There is a stop just outside of the airport. The service works all day on a regular basis. A detailed schedule (Line E) can be consulted in this link. Price: ~2.00 euros, including the price of the card (0.60 euros) that can be reused. Note that the metro works on an open system (no barriers that will open only upon presentation of a ticket) but controls are frequent. You need to be in possession of a validated ticket (tickets are validated before entering the train), otherwise you may be fined. For further details, see the Metro do Porto webpage.
By taxi: There is a taxi line just outside of the airport. It will cost you ~20 euros to reach the city center or the train stations.
Travel from Porto City Center to Lamego
By train: Probably the nicest way is by train (Porto-Régua, ~10 euros) + taxi (Régua-Lamego, ~10-13 euros). There are regular trains leaving Porto-Campanhã (every 2 hours during the day) to Peso da Régua (the closest train station to Lamego). Details on the timeline can be found here. Once in Régua (12km from Lamego), the best option is likely to take a taxi.
By bus: Another option is to take a bus from Porto to Lamego. The price is ~11 euros for the ticket (one way). As an example you can find timelines and buy tickets in this link. For this specific option, the bus station (Rede Expressos) in Porto is next to the metro station Campo 24 de Agosto.
By car: If you are renting a car, Lamego is ~1h30 distance from Porto if you take the highway option (A4 to Vila Real and then A24 direction Viseu). For a more scenic road with some amazing views of the Douro Valey, we can recommend to leave the A4 highway after Amarante and take the (winding) road to Régua passing by Mesão Frio.