Several airlines flight to Brazil from North America, Europe and Asia. From several cities there are direct flights to Rio International Airport named after “Antonio Carlos Jobim”, a famous Brazilian composer who wrote the song “The Girl from Ipanema”, believed to be the second most recorded pop song in history. In Rio, there is also a regional airport, named “Santos Dumont”. Unless you have a stopover in another Brazilian city, you will most likely disembark at the Antonio Carlos Jobim Airport, also known as Galeão Airport.
When you disembark you will pass first through Immigration and then Customs. There are official taxis that you can pay in advance a fixed price (around US$40) and there are taxis that run on meter. These will cost you about US$25. The advantage of pre-paid taxis is that you can pay by credit card and the price is fixed, independent of traffic jams, common in the route from the airport to the hotel, early in the morning. In normal road traffic conditions, it takes about 35 minutes.
There is also a special bus line that leaves the airport and stops at Atlântica Avenue, except on Sundays and Holidays when it stops in a parallel street (Barata Ribeiro), three blocks from Atlântica Avenue. The bus company is called Real, Line 2018 (Aeroporto Internacional do RJ/Alvorada). Buses leave at every 30/40 minutes. It costs R$16 (US$4, approximately). You pay cash (in Brazilian Currency) directly to the driver.
Additional information about the airport transportation can be found here.