Portugal is relatively easy to play. It is a good country to play for a first game, as it gets to do all the things that the game is focused on, some of them quite early. Because of its isolated position in Europe, and its historically early interest in colonization, playing Portugal doesn't force you into difficult battles for existence and expansion.
There are some themes to a game as Portugal that you should keep in mind while playing as this country. The first theme presented right from the start of the Grand Campaign in 1419 is subjugation of North Africa. The second theme is colonization, forcing the player into a choice of directions to pursue. This will lead to the Trading Empire v. Colonial Resettlement theme; Portugal deciding on what to do with its settlers. The late 1500's and early 1600's bring the Spanish Dominance theme to the front, as historical events bring Portugal under Spanish influence and control. Finally, Portugal faces the theme of Avoiding the Decline, where historically Portugal battled to avoid losing its productive overseas colonial empire, facing such up and coming powers as the Netherlands.
Portugal begins the 1419 scenario at war against Fez and Algiers. To begin the siege of Tangiers, split or reorganize the troops stationed there. Use your fleet to bring Pereira and your other 20 troops into the war. (Algiers may land troops in Portugal, but as long as you take Fez's 2 provinces before all 3 of your provinces fall it doesn't matter). Most players like to take Tangiers, but in general North Africans make better vassals than subjects.
Exploration and Colonization
Which direction to explore is up to you. The historical route is to explore the African coast and the route to India, but an argument can be made for going west: you have the Azores as a starting point, and you'll have all those Caribbean sugar islands to yourself for several decades. Also as Portugal you can annex the Aztecs without getting the state bankruptcy event, and colonize the gold and wine provinces of California.
If you take the historical route, build colonies to act as way stations for your ships so that they don't take so much attrition. Colonize islands where possible (Cape Verde, Fernando Po, Mahe). It also helps to have military access to one of the pagan nations on the coast of west Africa; this is where obtaining Morocco's maps pays off. Morocco knows Songhai, and Songhai knows Ashanti, Dahomey, and Benin. Bribe one of these last three with state gifts until they agree to give you military access.
Most colonizable African provinces are bad investments income-wise; they are expensive to colonize, have low-value goods (mostly slaves), and low tax values. Those you use as way stations should be left at level 1. The Cape area is one exception: it has several good provinces (Table/Karoo/Ciskei). Ivory is a second exception, although you can get most of its value from trading posts. Still, especially later in the game, with high infrastructure technology the production income from ivory will be quite large, and colonies on ivory will pay off.
Once you've explored the Indian Ocean, start colonizing India and the Spice Islands. Use your conquistadors to take Zanzibar and any other centers of trade you can grab.
The safe strategy is to ally with Spain/Castile and keep Spain happy throughout the game. You'll want to use your cash for colony building, not standing armies, so let them pay for your defense.
On the other hand, Castile has lots of high-population, same-culture provinces that would make excellent additions to your territory. If you decide to take provinces from Castile, ally with Aragon so that Castile has to fight a two-front war.