For me and my wife (before our son was born, of course!) we usually read about 50% of the daily newspaper (Publico) and just about 100% of the weekly one (Expresso).

We usually would take the newspaper to the beach or a cafe, spend a few hours there just reading the paper (trading sections every so often) and chatting a bit about what we were reading. It was as nice ritual.

I imagine it's like any large new source of entertainment/knowledge. At first, you'll not quite know what is interesting and worthwhile and what isn't, and will use guides to help you find what to read, and your forays into exploring further will meet with mixed success, as you waste time on things that in retrospect weren't worth it. As you become more accustomed to to the resource, you'll eventually be able to get a good idea of whether you'll like something from the section, headline, and if it gets that far, lead. At this point, since you might be scanning the whole document before you are done, jumping to sections because of main page leads isn't worth it, you'll get there eventually anyway.