Metro. Rio's metro is clean, air-conditioned, safe and cheap. Two main lines connect the Zona Norte to the Zona Sul, running from around 5 am to midnight on weekdays. On Saturdays service starts later; on Sundays and holidays hours are more limited. A single ride costs a few reais. The metro does not reach all beaches -- for Barra da Tijuca you will need to combine it with the BRT.
Bus. Buses go everywhere in Rio and are very cheap, but routes can be confusing since there is no comprehensive map. Destinations are listed on the front of the bus. Air-conditioned buses (frescoes) run along the beachfront roads and are more comfortable. Hold on tight -- drivers are aggressive.
Taxi and ride-hailing. Yellow taxis are metered -- make sure the driver uses Tariff 1 (Tariff 2 applies after 11 pm, on Sundays and holidays). Uber and 99 are widely used and often cheaper than taxis. For airport transfers, pre-booked private cars are a calmer alternative.
Ferry. Ferries from Praca XV in Centro cross Guanabara Bay to Niteroi in about 20 minutes. The conventional ferries have open decks with great views of the Rio skyline and Sugar Loaf.