I switched out an old lighting fixture, attempting to keep all things the same, BUT, now the light won't turn off, my question, which wires are supposed to go to the switch? 1 black and 1 white? Where does the fixture black wire connect to? To the power source black, or to the switch?

If you have a white and black on the switch, you apparently have a switch loop that was unmarked, In the ceiling, the black wire, if it is hot all the time, connects to the white wire that comes from the switch. Put a piece of black tape or mark it black with a magic marker on this white wire. Connect the ceiling box white to the light and the black from the switch to the black on the light. In the wall box, connect the black to either terminal and the white to the other. Mark the white wire black with tape or a magic marker.