U8glib Code Help - Simple text display with new line
First, u8glib is no longer maintained. It has moved to u8g2.  There is a u8x8 mode that is much like the u8glib code, in that it is text-only, and uses fonts that fit in an 8x8-pixel box, though there are multiple fonts to choose from.

Second, u8g2 does not have an automatic scrolling mode, so the Console example you mention keeps a buffer (an array of strings, with one element per possible text-row on the display) of the "history". Each time it adds a line to the console, this example copies every line to the one closer to the top of the display, and then copies the new line to the last row (the bottom of the display.)

Go and do likewise. If you show your coding attempt, you will get better answers.