Flying
The nearest airport is in Faro. From the airport you have to go into the city approx. for 2 euros (15 minutes). From there it takes 1 hour and 20 minutes by train to Portimão, the ticket is approx. 7 euros. You can also take Uber from the airport to the apartment, it costs €50 and takes 55 minutes.
Lisbon airport is a little further. From the airport, you have to take two subways for approx. €3.6 to the FlixBus/Rede Expressos bus stop. From there it takes 3.5 hours to Portimão, the ticket costs approx. 15 euros.
The farthest airport is in Porto, the way from there is too long.
Train
In general, Google maps is good for checking timetables, but there are other ways.
To check the train schedule: https://www.cp.pt/passageiros/pt or Comboios application or CP application
However, to buy a train ticket: https://www.cp.pt/passageiros/pt or CP application
Bus
There are several bus companies, Google Maps lists the schedule and which company’s website you can buy a ticket on.
You can buy more complicated and connecting bus tickets here: https://www.busbud.com/pl
In the Algarve, the local intercity bus company is Vamus: https://vamusalgarve.pt/#/
Taxi
You should download the Uber app. The app shows in advance how much the trip will cost, it is always fixed, it never changes. Uber is very cheap in the Algarve, ubering between cities is only approx. 5 euros. It’s worth it.