When no button is pressed, all row inputs are high .
All column outputs are low, because my code has told them to be.
If I press a button, all columns are still low and one row is forced low by the button press. I then set the first column output high. So there will at this point be one column high and and the rest of the columns are still low.
I then look to see if the row input which was initially forced low by the button press is now forced high due to the button still being pressed and the column output being high. If not, I set the first column output low again and move to the next column output and start over. In this way, there is never more than one column output high at a time.

I'm sure there's nothing revolutionary about doing this, but that's what I'm doing, and it works, and I don't really know how to explain it any more clearly. The columns are always outputs and the rows are always inputs.