Disclaimer: I do not own Harry Potter.
It took a while for me to get the hang of this dark wizards hunting thing. And it really was hunting. They were my prey and I was the great predator that evoked their flight response.
Initially I tried using my more common senses. Sight, hearing, even smell. There were times in my hunger that I could smell the souls of wizards from ever greater distances. The chance of a mistake or collateral damage trying to narrow the search to my desired meal is what led me to finding alternatives, however.
That's where my residents came in. As their jailer and new Master of Death, their knowledge of the criminal world allowed me to greatly narrow my searches. At this point, my own combined senses of wizard, dragon, and dementor, could locate and track the most vile individuals.
Unfortunately my cold depressing aura and magical might was also detectable by them as well. And so the hunt would begin with me searching for a possible location for dark wizards, getting the scent of a meal, and they, trying to flee before I gobbled them up. With each successful hunt, the process would repeat with newer, more up to date information.
It wasn't easy. The hunger was an almost constant itch that needed to be scratched, even if I apparently didn't even need to feed to survive. Resisting the urge to feed on the nearest group of souls made me even a little bit sympathetic to the dementors. However much they called me a monster and attempted to get the public and governments to hunt me in turn however, I would not become a monster. I am not what I eat. I am the power of my dark enemies turned against the rest of their kind, and I will not allow it to be used as it once was ever again. Not that it seemed to keep them from trying. They even believed they could stop me at times.