The four largest mobile phone companies in Brazil are Vivo (Telefônica/Portugal Telecom), Claro (América Movil), TIM (Telecom Italia Mobile) and Oi (Telemar).
You can normally use your foreign mobile (celular) in Brazil as most European countries or the US have roaming contracts with Brazil. You can call or be called in all GSM networks. The Brazilian standard is the American TDMA or CDMA.
Mobile phones are available throughout the country, either in general mobile shops or in the shops of the mobile phone companies. You can choose between pay as you go (pre-pago) or a monthly plan subscription (pos-pago). In either case you will have to provide certain documents. As the competition between the individual providers is very high, they constantly outbid each other with offers and promotions. So check and compare the current offers and chose a company that suits your needs.
Pay as you go
Prepaid, or pay as you go cards, are a good option when you are new in Brazil. They are much easier to get than a contract and they prevent you from racking up high bills while you are becoming familiar with Brazilian telephone costs.
In order to buy a prepaid card it is mandatory to provide your CPF number. However, as with most things in Brazil, you will notice that prescriptions are not always taken that seriously. So if you want to buy a prepaid card before you obtain your CPF number, try different shops. You will most certainly be lucky eventually.
Note that prepaid cards are automatically deactivated if not in use for 3-6 months.
Monthly plan subscriptions
The required documents to obtain a monthly plan subscription are much more extensive. If you just arrived to Brazil or are a non-resident you might therefore opt for a prepaid card. For the phone contract you have to provide either a lease contract or a payment of your property tax, a salary statement, cable TV bill and, if applicable, licensing documents.