Official taxis in Rome are white and have a Rome crest with the taxi number clearly displayed on the front door. Beware of the illegal taxis who are often also white.
The fixed fare for a Rome taxi is €48 between Rome Fiumicino airport (FCO) and central Rome (within the Aurelian walls) for up to four people and their luggage. The trip takes approximately 45 minutes to most parts of this central area, however your journey will depend on unpredictable Roman traffic, even worse if it’s raining.
If your accommodation is outside the central area, you will have to pay whatever is on the meter.
When you are in the city, taxis are not really supposed to stop if flagged down. They sometimes do, but your best bet is to find a taxi rank. Getting in the cab at a taxi rank will also save you money. If you call a taxi, the meter starts from wherever the taxi is sent from.
If you need a cab to come to pick you up, you can call in advance. Few of the best companies are Radio Taxi with the number +39 06 3570 and Taxi Samarcanda with number +39 06 5551.
You can also download MyTaxi. The taxi app allows you to order a taxi directly to your location without having to speak to a dispatcher in Italian. It will send whichever taxi is closest from any official company. Just keep in mind that the meter starts from wherever the driver accepted your request.