No secondary button (right click) on touchpad

Solution 1:

Basically, Ubuntu 18.04 currently defaults to "Mac" behavior on the touchpad. The technical details are that Ubuntu defaults libinput touchpads to "clickfingers" behavior.

To revert that, run this in a terminal:

gsettings set org.gnome.desktop.peripherals.touchpad click-method areas

Another option (thanks OP) is to install gnome-tweak-tool (either through your software manager or through sudo apt install gnome-tweak-tool in the terminal). Navigate to the “Keyboard & Mouse” sub-menu in the left menu of gnome-tweak-tool, and select “Areas” from the touchpad’s “Mouse Click Emulation” options in the right side panel, as shown in the red box in the image below:

[Warning: This fix is for the libinput driver that ships as the default input driver for Ubuntu 18.04. YMMV if you've installed the (different) synaptics driver before trying this fix.]

Solution 2:

Right button event is generated when two fingers are held down on the touchpad when a physical click is generated. The location of the fingers does not matter and there are no software-defined button areas.

This is the default behavior on Ubuntu 18+ and Apple touchpads.