I’ve not seen the ‘dry wine’ references but since Port is very sweet (to me), it might be to differentiate between table wine and port.
In Gaia, across the river in Porto, are many Port lodges. A number of them also have regular wine for tasting. Try looking at the websites of the larger ones. I did a flight of tasting a number of years ago but can’t remember the name of the lodge.
There is likely to be wine restaurants in Porto (we have one in Cascais), that will do tastings and a bit of education on Portuguese wines.
You are wise to want to do tastings as the Portuguese wines aren’t labeled with the type of grapes and it takes a bit of time to learn their labeling. You might also download the Vivino app. You can take a picture of a bottle and get descriptions of the taste, reviews, etc.