If you are only here for a short while, taxis and Uber are the way to go.
Taxis
Taxis are pretty expensive here and, if you are a gringo and don’t know your way around, even more so. The trip from the airport to your hotel will take ages and resembles more a city tour.
The taxis are generally clean but do not expect the drivers to speak any English. The price of the ride is displayed in front so you can see it. Never take a ride in a taxi that doesn’t display the price or the driver says that it doesn’t work.
Uber or 99
Uber or 99 (another local ride-share) is the way to go if you do not have your own transportation. They are plentiful, the drivers are very friendly, the cars are clean, and they are cheap. And because you can follow the route on your own phone you can check if they go the most direct way.
Many of the Uber drivers speak some English and, if they hear you are a gringo, are eager to speak with you. If they talk to you, just have a chat with them; you will make their day. It is also not uncommon to have gringos driving Ubers as it is a way for them to make money.
Please give us some feedback on what experiences you had with taxis and Ubers in Brasilia in comments below.