No secondary button (right click) on touchpad

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.]

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.