The subways in Rio are comparatively cheaper, safe and also very efficient. If you are planning to visit many places in a day then combination ticket options are also offered for the convenience of the travelers.
Rio de Janeiro has about 831 public bus routes that connect all the places in and around the city with each other. The buses are inexpensive and most of the buses have a number associated with them. However they are mostly closed down during the night and are often infected by pick-pocketers.
The taxis can be a great help to reach those out-of-the-way places. Their rates are reasonable but the tariffs during the day are different from the tariff at nights. The taxi service in Rio is also a safe option to choose at night.
Rio can be best explored on foot and the places like Lapa, Santa Teresa, Centro and Zona are especially pleasant for a walk. The people are helpful and can guide you along the way. So get your sneakers on and get going.