Ubuntu 18.04 Enable Tap-to-click on Unity desktop

Well, I don't know if Unity has some option for it, hopefully someone will answer on that one. But you can enable it from command line:

1. list devices with xinput list, and find the touchpad name in the output.
2. use a xinput set-prop "SynPS/2 Synaptics TouchPad" "libinput Tapping Enabled" 1, where the text in first quotes SynPS/2 Synaptics TouchPad needs to be replaced with touchpad name you got in step 1.

This will only work till reboot, so you'll need to add the command from step 2 to autostart.

Late Answer for those who see themselfes stumbling in this wide narrow sea.

If you are using a Synaptics device best thing would be installing the Synaptics drivers - The options you need will be added to the general settings under "Mouse and Touchpad".

EDIT: Apparently xf86-input-synaptics is not a synaptics driver, but still did the job for others and my machine(xps15).

To do so, first update everything

sudo apt-get update

and install the driver with

sudo apt-get install xserver-xorg-input-synaptics

In case that doen't work because you are missing dependencies, go for the HWE version;

sudo apt install xserver-xorg-input-synaptics-hwe-18.04

finally, restart and you should find the extended standard options in the system settings.