The bus public transportation, STCP, in Porto, is a wide network of routes, inside and around the city and you can travel almost everywhere. This is a cheap and reliable option.
Porto also has a metro transportation system. But do check all the stations. They do not cover the entire city of Porto.
You can buy a rechargeable ticket, the Andante Card, that will allow you to use the bus and metro transportation.
If you rather travel by taxi, it’s a very viable option, more confortable than the public transportation system, but more expensive. For european standards, it’s an affordable transportation. You can call Radio Taxis or Taxis Invicta. It’s a telephone booking system. Just let them know where you are in Porto and a taxi will arrive in a few minutes.
You can also rent a car. Check these options: