How do I disable the touchpad while typing?

I suggest installing libinput it has much better "disable while typing" and "palm detection" algorithms.

Run

sudo apt install xserver-xorg-input-libinput

and restart the GUI session, or reboot.

If you need "tap to click", you can add

Option "Tapping" "true"

to the touchpad section of /usr/share/X11/xorg.conf.d/90-libinput.conf.

All options can be found on the manual page.

If you are using Ubuntu 16.04 with the -hwe-16.94 stack, you will need to install xserver-xorg-input-libinput-hwe-16.04 package instead of xserver-xorg-input-libinput.

You can check which HWE stack is installed by checking if xserver-xorg or xserver-xorg-hwe-16.04 package is installed.

For Ubuntu before 17.10 (Unity)

Open System Settings -> Mouse & Touchpad : in the Touchpad section switch from ON to OFF

Additional information for other users reading this post: The answer was written before the content of the question was changed, originally the question was: "An actual solution to disable touchpad? I just want to disable the touchpad completely, no scrolling, no moving the cursor, nothing.". So the answer from @Pilot6 is the much better solution for what the current version of the question is asking about!

You can also do it with Synaptics.

synclient PalmDetect=1

That will not be permanent, but you can do this by creating or editing the following file and adding Option "PalmDetect" "1"

# /etc/X11/xorg.conf.d/70-synaptics.conf
Section "InputClass"
  Identifier "touchpad"
  Driver "Synaptics"
    Option "PalmDetect" "1"
EndSection

https://wiki.archlinux.org/index.php/Touchpad_Synaptics#Disable_touchpad_while_typing