A great and least expensive way of getting to Manaus is by booking a Lloyd Aereo Boliviano flight direct from Miami. We found we could get a first class or executive seat for less than coach on other schedule airlines, many of whom travel via Rio. The downside is its not a daily flight and it reaches Manaus in the early hours.
Sadly in 2013 it seems this routing is no longer available so the best prices for a direct flight are AA TAM or via Panama on Copas Air
Manaus may be a city of more than 1.5 million people, but it is still very remote and isolated from just about everywhere else. Waaaaah! ***NO MORE FLYING HERE DIRECTLY FROM MIAMI***, at least until Varig reinstates that route...oh please, please, please!?! Coming from North America then, you will likely have to backtrack down through Sao Paulo and back up again. C'est la vie. No one said it would be easy to reach this city primeval. And really, would you love it as much if it were a cakewalk?