Local taxis are available in most Brazilian cities of any size and most all are metered. Just make sure you always use a legitimate taxi. This is pretty easy if you have your hotel or restaurant hail or call a taxi for you (they know), only use taxis that are lined up at a ponto de taxi (taxi stand) or call a radio taxi service.
Taxis from the international airports in Rio de Janeiro and São Paulo to various locations in the city are usually contracted on the basis of a flat, one way charge although, to make your departure easier, you may want to buy the round trip upon your arrival. There will be a kiosk or booth at the airport for these taxis and either cash or credit card payment is usually accepted. In Rio, do not contract with an independent taxi (who may be very friendly and show you a printed price sheet) because their fare from the airport to, say, the Copacabana area may, in fact, prove to be at least twice the real fare.
With the exception of Rio de Janeiro where a 10% tip is the norm, tipping taxi drivers is not usual except for rounding off the metered fare to the nearest real and letting them keep the change. If a taxi driver totes heavy suitcases or packages for you, it is appropriate to leave them a couple of reais para um cafezinho (for a little coffee) or, for a little larger tip, para uma cervejinha (for a little beer).
Numerous Brazilian cities also have moto taxis which are pretty much what the name implies: put a provided helmet on your head and hop on behind the driver for your taxi ride. Moto taxis are inexpensive at about R$ 5.00 for a short trip. If you want a cheap adventure, this is for you.
Most Brazilian cities of any size have local buses with interconnecting routes that cover the entire city. Bus fares are normally reasonably priced at around R$ 2.00+ to R$ 3.00+ and transfers are available.
Both São Paulo and Rio de Janeiro have extensive metro (subway) systems. Unlike what you may be used to in North America, the metros in São Paulo and Rio de Janeiro are graffiti free, clean, fast and efficient, and often provide the best way to get around these two often congested cities.