While the internet has made things easier, it is not the end-all of information. Newspapers do still deliver copies every day, and this can be helpful for keeping you up to date on important issues. The reason for this is because it gets you into a routine, and you can have it ready for when you have time to read.
Of course if you are on the go more often than not, you can consider finding information feeds online. These are very similar to the idea of the paper, but instead can be sent directly to your computer or smart phone. This is a solid option for those who have busy lives or long work hours.
You might also consider visiting a bookstore or a newsstand when you are out in the morning or afternoon. These places receive magazines as well as papers, which will contain more focused information useful to you. Again, routines are key for developing habits that lead to easy info-gathering day to day.
Perhaps one of the best ways to keep up, though, is talking with other people. Finding someone who is also interested in daily developments and having a conversation with them is an opportunity for you to inform each other of what is going on. This is not only a means of learning, but also gaining insight into different perspectives.
Hopefully you can see now that for finding daily stories and news articles you have a wide variety of options day-to-day. Keep in mind that while you may not see it coming, it can happen that recent information will become extremely important. Good luck with your ready and enjoy it.