Metro system, Rio de Janeiro

When you arrive in the airport, there's no way of reaching the civilized points of the town out of cab. The price of the cab is around R$40, about US$10.30: ask to the driver FIRST how much it will be. This can avoid a small problem (they are not roman cab drivers, but you'd rather ask first).
Use the metro system whenever you can. I would choose a hotel close to a metro station.
Bus system works fine in Rio, but the stops don't have names like some European cities.
Charming trip: take the ferry, in Rio downtown. You can choose the "sister city" of Niteroi, with its impressive Contemporaneous Art Museum, or the Paqueta Island. The trip is charming, and you can use the "jumbo" ferry if you want to move fast (Rio-Niteroi in 4 min). If not, 20min to reach Niteroi. There, to get to the museum, take the 47B bus.

MEtro Service in Rio is great for travellers, it has only two lines, but it connects the places you need to see in Rio from the main Hotel areas and beaches.

A single ticket is 1.88R$ and you have option for a return ticket or a 10 ride ticket. it is open from 6am to 11pm and service is very fast, also is the safest way of moving around.

The Metro System in Rio is so simple, anyone can take it! Yes, even you!
Okay, okay, I admit, I once got off in the wrong Estaçao, but I wasn't paying attention :-/
Whenever you're reaching a new destination, the intercom lets you know what it is. I have been in only one metro that was better, and it's the one in New York.
Please note that in the weekend some stations are not reachable! I had this once with the metro station closest to my hotel...
It's also very cheap; e.g. only R$1.88 for a simple ticket, R$3.76 for a double. When you're going on the metro and then onto a bus, buy a combi ticket (integraçao). It's cheaper and less hassle.
Tickets can be bought inside the metro station, but also to vendors on the street. I think it's a kind of 'second job' to earn extra cash. When you can, buy it from them.
Another nice thing about the Rio Metro: when you're inquisitively looking in your travel guide, locals will uncessantly come to you and tell you which way you should go. Brazilians are very helpful...