If you are looking for a relatively inexpensive, safe and convenient way to travel, tapping into Quito's extensive taxi network is a good way to get around the city.
During the day, taxi drivers are required to use a taxi metro (or meter) when they drive you around. When you climb in, the initial rate should be 35 cents. Always ask for the metro, which is typically located just in front of the emergency brake, between the driver and front passenger seats. You should always be able to easily see the meter and should check the amount as you arrive at your destination (before the taxista turns it off).
Some drivers have been known to tell passengers that their meter is broken or that they don't have one, particularly around large hubs such as Terminal Terrestre. Taxis are plentiful enough that, if your driver won't use his meter (or has a meter that seems to be going extraordinarily fast), tell him to stop, get out and hail a more honest cabbie.
Most daytime trips around the city cost between $1.50 and $3. A trip from anywhere in Quito to the airport should cost no more than $5-$6; the trip from the airport is usually around $7.
At night, rates increase by $1 (since few other public transportation services are available) and taxi drivers do not use their meters. Make sure to negotiate a price before you get into a cab. If the price is too steep, ask for a more reasonable rate or hail a different taxi. Drivers charge per ride, not per person.
Make sure when you're taking a taxi that you have roughly the correct fare in small change. Most cab drivers will not have very much money on hand and will not be able to handle large bills. Tips are also accepted but usually not expected.