As in many aspects of physics research, even in the absence of positive data one can learn things by asking the right questions about negative results. In this case the question is "Given that we have not yet detected this planet, where could it be?" rather than repeatedly asking "Is it there? No? Ok how about there?" at various points in the sky.
There are a number of telescopes that scan the sky looking for various things (well, that's basically what telescopes do...I'll refer to these as survey telescopes to distinguish them from telescopes like Hubble that look at specific targets when directed). There is one called WISE that is looking for distance planets and nearby brown dwarves (distant from the solar system's perspective and nearby from the galaxy's). So they consider where this planet could be and not be detected by WISE. The same goes for other survey telescopes: one called CRTS, one called Pan-STARRS, one called the Dark Energy Survey. Another group of researchers, in the time since the January announcement, did an analysis of Saturn's orbit given hypothetical perturbations from this planet, and used the fact that Saturn and the asteroids have not been very perturbed to rule out a few more regions.
What remains is a band of sky where Brown and Batygin's analysis shows this planet must be in order to explain the orbital alignments of the trans-Neptunian objects, and various regions of that band are excluded from these various non-detections.
Where is this big region on the actual sky? I have approximately traced it out on a sky map, which is shifted 180 degrees compared to the image above. In the Northern hemisphere, the big region encompasses Orion, which is one of the easiest constellations to find!
So, by looking in this region, it could find this new planet, or it could rule out its hypothetical existence.