The most likely explosive event to occur at Yellowstone is actually a hydrothermal explosion (a rock hurling geyser eruption) or a lava flow. Hydrothermal explosions are very small; they occur in Yellowstone National Park every few years and form a crater a few meters across. Every few thousand years, a hydrothermal explosion will form a crater as much as a few hundred meters across.
Though the worst-case scenario for a giant Yellowstone eruption is indeed bad and could have global implications, most past eruptions at Yellowstone were not highly explosive. Of the past 50 or so eruptions, almost all were simple lava flows. If they occurred tomorrow or next year, they would have minimal direct effect outside Yellowstone National Park.
As for the worst-case scenario, even previous Yellowstone supereruptions did not cause extinctions, and ash fallout on the other side of the continent was minimal.
Yellowstone is routinely monitored for signs of volcanic activity. These methods include using seismographs to detect earthquakes and using GPS (Global Positioning System) to detect ground motion. The USGS has not detected any signs of activity that suggest an eruption is imminent.