My guess is you have a switch loop here. In this case, you would have 2 romex cables coming into the ceiling box. One cable is the input line and is always hot. The other line goes down to the switch. The one going to the switch probably has some sort of black marking on the white wire. This indicates that this white is not a neutral, but is being used a a hot.

At the switch, you'd see both the black and the white with black marking attached to the switch. When the switch is on, it connects both wires.

Before you go to far you should use some sort of connecting testing to confirm if you have a switch loop or something more convoluted.

If you have a switch loop, you would normally wire the ceiling box like:
- Input black connects to switch loop black
- Input white connects to lamp white
- Switch loop white (with black marking) connects to lamp black
- All grounds connected together

Here's a diagram that I found:
https://www.diychatroom.com/attachments/f18/45554d1328773102-switch-loop-wiring-switch-loop-extension.jpg

I don't recall if there's code regarding whether black or white marked black should carry hot to the switch. My preference is to use the black wire.