I read most of my news with an RSS newsreader (the free RSS Owl). I pick up my local newspapers, Yahoo, New York Times, CNN, NPR, etc. I also subscribe to a variety of retirement related RSS feeds, environmental feeds, Engadget, Lifehacker, Crunchgear, etc. I currently subscribe to about 30 feeds and can read through them all in 30 minutes or so, usually less.
Unfortunately, RSS seems to have fallen out of favor. You either have to link through Facebook or Pinterest, have the news sent by email, or visit each site individually. I don't have time for that.
Forums are similar. Things were so much nicer back in the Usenet newsreader days. I could read and participate in numerous subjects quickly and easily. Now I would have to visit each forum individually, logging in to each one, and checking for new posts. Who has time for that? So, Early-Retirement.org is about the only forum I visit anymore. There are others that interest me, I just don't have time to visit them.
I watch local TV news at lunch time, and national news in the evening. That's it.
I have a direct link to the weather page of a local TV station on my desktop so I can quickly look at the weather forecast when I need it.
On rare occasions (when we're visiting family and I'm bored), I'll use Google News on my phone to read news. But I can't really customize it, I read whatever they decide to send me.