As a visitor, you may want to use a cab as a more comfortable option to the public bsses. For your safety I put together some advice locals and other travelers gave me for my stay in Ecuador.
First rule: If you are able to speak Spanish, you will pay less. But do not worry; most taxi drivers will understand at least some words of English. The ability to negotiate prices in Spanish however will get you into a preferable position. Ask the locals or other travellers for common routes, e.g. from the Mariscal to the Teleferico and what they ended up paying. In most cities a higher night tariff will apply. When you are in Quito, make sure the driver has a taximeter during daytime and that it is turned on once you take seat.
Second rule: Never get into a car before you set the destination and price. Once you are in they will ask automatically for more.
Third rule: for optimal safety, do not stop a taxi at the street. It is safer to call a taxi company for a cab, because the drivers are registered then. The favourite company of my Ecuadorian friend Gabi is: (+593)22639639
Fourth rule: do not get into a taxi if it has no badge on the windscreen, at least follow this if you do not want to waste time making a call and order a cap.
Fifth rule: do not share a taxi with strange persons, always take your own or share it with people you know.
Sixth rule: Use your mind and common sense, I drove with a drunk driver because I was stupid and did not smell it in the first place.