(a) The kernel is told about the change using the ioctl VT_RESIZE. This causes the kernel to reallocate console screen memory for all virtual consoles, and might fail if there is not enough memory. (In that case, try to disallocate some virtual consoles first.) If this ioctl succeeds, but a later step fails (e.g., because you do not have root permissions), you may be left with a very messy screen.
The most difficult part of this is (b), since it requires detailed knowledge of the video card hardware, and the setting of numerous registers. Only changing the number of rows is slightly easier, and resizecons will try to do that itself, when given the -lines option. (Probably, root permission will be required.) The command resizecons COLSxROWS will execute restoretextmode -r COLSxROWS (and hence requires that you have svgalib installed). Here COLSxROWS is a file that was created earlier by restoretextmode -w COLSxROWS. Again, either root permissions are required, or restoretextmode has to be suid root.
In order to deal with (c), resizecons does a stty rows ROWS cols COLS for each active console (in the range tty0..tty15), and sends a SIGWINCH signal to selection if it finds the file /tmp/selection.pid.
Finally, (d) is dealt with by executing a setfont command. Most likely, the wrong font is loaded, and you may want to do another setfont yourself afterwards.