This question always baffles me whenever it comes up. I don’t think I use the internet in any special way. But maybe the following is news to someone:
Most websites that update regularly emit a kind of file called RSS, which can be captured by things called feed readers, that gather them up and save them. Google Reader is a feed reader. It’ll collect up all those RSS feeds and present them to you in a way that lets you read all the websites you’re interested in on a single page.
So all you do is get the RSS of a website that has interesting stuff and shove it into your feed reader.
I use Google Reader. I also use an iOS app called Reeder that links into Google Reader. And, every day, wherever I am, I read as much of what Google Reader captures as I can.
I also read a newspaper every day, and I read the BBC Online news every day, and watch BBC Newsnight most nights, and a few magazines a week, and — perhaps most importantly, these days, I have a well-tuned Twitter feed full of people who like to post links to genuinely interesting stuff. Let me reiterate that bit: for FREE, you can arrange for a bunch of well-connected strangers to push interesting news to your screen, LIVE, updating every second.
So, that kind-of acquaintance whom you feel you should follow but whom talks mostly about sandwiches and the shape of his turds? Dump him and add @qikipedia or @brainpicker instead. To start with.
I would also point out that you can do the same thing on Tumblr. There is no natural law or official quota that means you have to do nothing but scroll through a bunch of shit cat macros every day. Tune your digital environment until it brings you all the good stuff.