Grub is a boot loader, i.e. the software that is launched when the computer starts and whose role is to boot an another operating system. So, unless I have misunderstood, what you want is not seeing the messages from Grub, but instead you want to see the messages from Ubuntu itself during the boot process.
Generally speaking, what you have to do is to remove the "quiet" Linux command line option. However in recent versions of Ubuntu, this is not enough because the splash screen has not been designed to display activity. Therefore, you also need to prevent the splash screen from starting up, and you can do that simply removing the "splash" command line option.
In other words, you should edit some configuration so that your /proc/cmdline changes from:
BOOT_IMAGE=/boot/vmlinuz-... root=... ro quiet splash ...
to:
BOOT_IMAGE=/boot/vmlinuz-... root=... ro ...
To do that, you need to set GRUB_CMDLINE_LINUX_DEFAULT in /etc/default/grub to an empty string:
GRUB_CMDLINE_LINUX_DEFAULT=
We are almost there: now you need to remove the so called gfxpayload and vt_handoff. While these two options improve the boot experience, they will also prevent your messages from being displayed. AFAIK, there are no options in /etc/default/grub that you can tweak for that, so you are forced to open /etc/grub.d/40_custom and add the following at the bottom of the file:
function gfxmode {
set gfxpayload=
set vt_handoff=
}
Simple, but effective.
