Getting around, Manaus
It cost 50 reals to take the cab from the tropical hotel to the opera house. I am sure you could take the bus but it looked pretty crowded and all the stops that it would make inbetween did not look like great areas. There was a big military presance in town.
It is not difficult to know your way around Manaus.
Still, if you can, avoid taking buses, for foreigners it is a little complex and you will seldom find someone who speaks enough english to give you directions (actually, Manauaras are not very good at giving directions).
If you can, rent a car, but be ready for the crazy driving!
Taxis have taximeter, so, you only have to pay what is in the meter. Tips are not expected.
The traffic is dangerous and disorganized. To rent a car is therefore not feasible unless you are a daredevil driver. Taxi drivers are rather expensive in Manaus and not very trustworthy. They will try to rip you off. But if you are not on an organized tour, which provides for a private bus you might have to use a taxi because public transportation is complicated and disorganized too.
for making tours on the rivers or in the jungle i suggest you reliable tour operator