What you'd do is scroll the screen (say for example by 1 pixel every frame), and have a counter that would start at 8 (in this example) and you'd draw one character from the scroller when the counter reaches zero, then reset it back to 8.
Also keep the VRAM address you're writing the scroller to in memory, once you've written 32 bytes then reset it back to it's original value.
But the way of doing it differs a bit, depending on what kind of mirroring you're using. With horizontal mirroring, you'd set the 'disable left 8 pixels of BG' feature, and with vertical mirroring you'd need to write to either both nametables at once, or in sequence.
I hope that makes sense.