Local buses are cheap, frequent and reliable. On the routes you are likely to take as a tourist, they are also safe. Most are R$1.85 for a single journey, but some that are air conditioned or travel longer routes can charge up to R$3.80.
The hard part is understanding how to use the buses. The names on the front are the names of the route, which is usually a circular route, not where the bus is heading to. That means you need to know the name and number of the bus you want, and the direction the bus you catch should be going in.
Fortunately, the buses you are likely to use as a tourist are likely to be limited two or three:
From Boa Viagem to Recife Antigo Map Link
To get to Recife Antigo, take a number 32 Setubel / Conde da Boa Vista bus, which is a regular bus, or take a smaller Air Conditioned bus, the 42 Airport / Conde da Boa Vista bus. When going to Recife Antigo, they take a similar route. You pick up the bus from any stop in the main one-way avenue Consilheiro de Aguiar. At the end of the long avenue the bus takes a left into Av Eng Antônio de Góes. This road takes a bridge over a river before turning right at the marina, and onto the long avenue, R. Eng José Estelita, which runs alongside the estuary. The road goes over a small pass-over. Along this route you will see the two large apartment buildings overlooking the estuary. A little after the apartment blocks the bus will cross another bridge onto the island of Recife Antigo. You can leave the bus at any of the three bus stops on the island before the bus crosses the river again.
As the bus takes a circular route, you will get back on the bus at the same stop you go off to return to Boa Viagem, but do not be surprised if you do not recognise where you are for the first 15 minutes or so of the journey. You will eventually recognise that you are back in Boa Viagem travelling along the other main one way avenue, Av. Eng. Domingos Ferreira, which runs parallel to the main avenue from which you left Boa Viagem. You need to look out for landmarks for where you want to leave the bus.
From Boa Viagem to Olinda Map Link
The bus from Boa Viagem to Olinda is the Piedade / Rio Doce bus. The journey time is approximately 30mins depending on the traffic. Look out for Shopping Center Tacaruna, and you are approx 5mins away. After the long, straight road, Av. Olinda, the bus bears right into Av. Sigismundo Gonçalves. Leave the bus at the second stop and cross the road into Praça do Carmo. As you cross the road to enter the square, you will notice the bus stop from where your return journey will begin. The square is one of the main entrances to the city and the start point of the Recife Guide Walking Tour of Olinda
From Recife to Porto de Galinhas
The bus company Empresa Cruzeiro operates a bus connection between Recife and Olinda. It departs from Rua Aveneida Dantas Barreto in Downtown Recife every 30mins, at 15mins to and 15mins past the hour, between 5.45am and 21.45pm. For tourists staying in Boa Viagem the best place to catch the bus is in front of the old airport building (to the left of the new one). For pick ups at this stop, you should add an additional 15mins during off-peak periods and an extra 30mins during peak periods to the departure time in downtown Recife. The price is R$4.60 each way and the journey time is approximately 1hr 30mins. Buses return between 4.10am and 19.55pm from the same terminus in Porto de Galinhas at which you arrived.
It is a standard bus, not coach, with no air conditioning or toilet. The new airport nearby has bathrooms you can use before you start your journey, and you may want to take your own drinks with you, although vendors enter the bus at points along the way selling drinks and other refreshments. On weekends, the buses can be very busy on the way there, especially at holiday times. My suggestion would be to take an early bus unless you want to find yourself standing the whole way there. The bus company phone numbers are 0800 81 2662 or (81) 2101 9000