Belém is served by Val de Cans International Airport (BEL), with regular flights to São Paulo, Brasília, Manaus, and Fortaleza. The airport is about 9 km from the city center; taxis and ride-share apps are the practical options.
By river, Belém is the eastern terminus of the Amazon river network. Passenger boats depart from the Hidroviária do Pará terminal near Ver-o-Peso for Santarém (two days) and Manaus (four days). Hammock class is cheap and genuinely interesting; cabins with air conditioning are available for those who want them. Bring provisions and a hammock if you are traveling in hammock class.
There is no practical overland connection to the rest of Brazil via road that competes with flying, though the BR-010 and BR-316 highways exist for those determined to drive.