If I'm at home then I browse on FeedDemon using its handy keyboard shortcuts, opening any articles that look interesting. If they look interesting/amusing enough to share then I save them into Delicious*. At work I use Google Reader directly, and if an article is not-work-safe, or too long to read over lunch/while code is compiling then I save it to Read It Later, a very handy tool that synchronises things I want to read later between my phone, and any PC I use regularly. The thing I love about it most is that on my phone it also provides a simplified text-only view which is much easier to read than 95% of websites***.
I used to save links direct from my phone to Delicious, but since that was taken over by a bunch of deluded simians their Android plugin has been abandoned, so I've switched to just saving articles to Read It Later and then sticking them on Delicious when I get to work/home.
I also get links via email (octopoid_horror sends me loads, and I get them intermittently from others as well). Some links come in via Facebook, which I read when I'm bored at a bus stop and have already read all my Google Reader entries. I used to get some via Twitter, but I've only been on there a couple of times in the last 6 months, and I really need to have a massive clear-out if I'm going to ever make it usable again.
And finally there's DW/LJ, where people have linkposts, or mention things in passing that I then reshare. You'll sometimes see a "via" in the link tags, and those are usually LJ usernames.
Every 15 minutes a job on If This Then That checks to see if there are new entries on Delicious and if so punts them over to Twitter, shortening the links with my bit.ly key so that I can see how many clicks they get. Once per day, at 11am (GMT) a job on Feed This To That takes the links from Delicious, filters them to the previous 24 hours, and posts them DW, which posts them on to LJ.
And then you get to read them. And point out the ones that are from 1997, clearly wrong, or otherwise should never have seen the light of day. Which is what makes it all worthwhile.
*A "feed" is a text-only version of a website, whereby each entry is separate from every other one. Rather than visiting a lot of websites multiple times per day to see if they've updated this is automated by a feed reader, which checks each one intermittently and displays new entries for you. And by "a lot" I mean 83. Which doesn't sound like that many, but includes things like the BBC front page, which had about 150 articles on it yesterday.
**I don't really like Delicious, but the best alternative is Pinboard.in, which doesn't use all of your tags for autocompletion of tags, and is case sensitive for tag completion too, which doesn't work well with my thousands of existing tags. They're supposed to be fixing that in the near future though, at which point I'll re-evalute.
***Similar to what Instapaper does on the iPhone.
Original post on Dreamwidth - there are comments there.