Portugal joins Civilization VI with the tools that have defined their gameplay over the series's history. A focus on exploration, diplomacy, and Trade Routes is this civilization's surefire path to a Science or Diplomatic Victory.
Casa da Índia
This ability is basically a direct buff to your Traders, since at least one other civilization will always have coastal cities unless you are playing on a map script like Inland Sea which severely limits access to water (which you should probably avoid as Portugal anyway). Even if these cities have less yields than the core cities you would normally send Trade Routes to, the innate buff to their yields usually allays this problem. Traders already have twice as much range over water than they do over land, so as Portugal your Traders will essentially have triple the range from the beginning of the game. You can even send them over water without Celestial Navigation, although you should definitely research this technology anyway since Lighthouses are the strongest building to construct if you want additional Trade Routes.
Some things to remember about the limitation of this ability are that it only affects international Trade Routes, meaning that you can still send Traders to your own inland cities, and that international Trade Routes do not necessarily have to cross water in order to end up in coastal cities.
Porta do Cerco
This ability not only incentivizes Portugal to explore far and wide, but also makes them better at it by giving units +1 Sight range. Portugal should be ushering Scouts out the door en masse as one of their first priorities, and those that pick up a Promotion should always take Ranger in order to see even further. Thanks to their civilization ability, however, a naval unit or two is also a good idea, to find civilizations with coastal cities that you can apply your extra Trade Routes to.
The Nau is emphatically not a combat unit. Its free Promotion should always be Helmsman, and once the Nau has this additional Movement its only purpose is to construct Feitorias. It is best to build a lot of Naus in advance before researching Steam Power, since their build charges do not carry over.
Feitorias are fantastic yield boosters for Portuguese Trade Routes, and with a lot of them in one foreign city the yields Portugal makes from trade can be astoundingly high. Unfortunately, however, they benefit the home city as well as Portugal, and thus it is best to construct them in city-states to avoid giving these yields to an actual opponent. Thanks to João III's unique ability, you have Open Borders with all city-states as well, so unlike major civs they can't just avoid giving you access to their tiles.
The Navigation School is an ideal supplement to Portugal's focus on settling water tiles. You will gain +1 point of Science for every two water tiles in the city. The theoretical maximum yield from this building is +8 Science, supposing both the City Center and the Campus are on one-tile islands, but this is not a realistic situation; more often the bonus will be around +3 or +4 Science, which is still quite strong. Education, the tech that unlocks this building, is in a slightly awkward place, but the bonus Science still offers quick access to Cartography and Square Rigging, both crucial technologies for Portugal. The yields from this building, along with bonus Science and Production from Trade Routes, make Portugal a fairly strong Science Victory competitor in the late game.
The Navigation School also offers benefits directly supplementary to Portugal's exploration focus in the form of bonus Production towards naval units and an extra Great Admiral point. Cities training Naus can make use of this bonus Production to help you get out more Feitorias, and various Great Admirals offer good bonuses for Portugal. Notably, Leif Erikson can help Portugal cross oceans without Cartography, a great exploration bonus.