Most of the tourist attractions in the city itself are within walking distance of each other and the major places to stay in the historical center. We live just outside the historical center and take a taxi only if we are in a hurry, have lots to carry, or are tired after a busy day in Centro.
There are many tourist attractions outside the city for which you have a variety of transportation options (individual guide or driver, guided tour, taxi, car rental, bus) that have been discussed in other threads that you can find by searching or asking a specific question here.
Taxis are readily identifiable, plentiful, and perfectly safe to hail on the street. Theoretically the light on top will be lit if the cab is free, but the drivers sometime forget to turn them on/off, so look into each cab that comes up. There is a cab line (sitio) in Centro at the north end of the Almeda (the park facing the Cathedral). If you have a card with your address or simply name the attraction you want to visit, the cab driver will get you there.