Sometimes it's quite hard to tell if an article is sensible, especially if you don't know much science. But there is one thing anyone can do, quite easily - and that is to check sources. I'll do this for the "Nibiru" nonsense stories so you can see how this works. The most unreliable and nonsense stories, as well as getting the science wrong, also tend to get their sources wrong as well, so this can be a good test to check for unreliable news stories.
As an example, a recent "Nibiru" story in the Daily Star says that a tenth planet was discovered in 1983.
Now you can go to one of the debunking sites, say to Phil Platt's "Planet X Saga: Science". He will tell you that the 1983 IRAS observation claim comes from a press conference. IRAS looked into the far infrared for the first time ever (blocked by our atmosphere on Earth). The astronomers said it could be anything from a tenth planet to a distant galaxy.
But how can you check that?
Well he helpfully gives links to the sources. Actually his page has a broken link so I had to do a bit of searching, but this is what I found as one of the original stories:
"A heavenly body possibly as large as the giant planet Jupiter and possibly so close to Earth that it would be part of this solar system has been found in the direction of the constellation Orion by an orbiting telescope aboard the U.S. infrared astronomical satellite. So mysterious is the object that astronomers do not know if it is a planet, a giant comet, a nearby "protostar" that never got hot enough to become a star, a distant galaxy so young that it is still in the process of forming its first stars or a galaxy so shrouded in dust that none of the light cast by its stars ever gets through. "All I can tell you is that we don't know what it is," Dr. Gerry Neugebauer, IRAS chief scientist for California's Jet Propulsion Laboratory and director of the Palomar Observatory for the California Institute of Technology said in an interview."