Leon is, for the most part, correct (I don't really see any errors in his logic there). There could be millions of black holes in the Milky Way or thousands or hundreds. We don't know. It is, however, theorized that a super massive black hole resides in the galactic center. And, although, yes, this is a theory. I believe it is correct due to what we see occurring there.
I took a high-level astronomy class on nothing but stars. We spent 2 whole weeks just talking about black holes.
Some people would argue that we don't even know if black holes exist. But, we do pretty much have all the symptoms and side-effects pointing to their existence. I'd say we have more evidence for the black hole in the galactic center than we have for any other black hole in the universe.