I skim the headlines, open interesting articles, give them a quick read, and save them to a bookmarking service.
When I have time, I go back to these saved articles to go deeper. Basically, I use the articles as a point to start from with the goal of reviewing relevant things that could benefit from more depth (programming, usually). I’ll read a book, build something, or go to a meetup to learn more and apply the knowledge.
This simple system works very well. I recommend this. It helps me stay both in the shallow and the deep end.
I work when I'm busy.
When I read I read what interests me.