The RTL8188eu WiFi chip is not supported in Raspbian Lite out of the box, so we need a few things to make it work, but I’ll show you how.

What do we need?

Unfortunately, you need a keyboard and a display connected to the Pi Zero to setup this, so you can’t go completely headless during the setup process. After successful connection to WiFi, you don’t need the keyboard and display anymore, and you’ll be able to use an SSH client on your computer to connect to the Pi. You need to connect the Pi to a display via miniHDMI adapter and HDMI cable, you also need a USB-OTG adapter to connect the USB keyboard to the microUSB port of the Pi Zero. You’ll also need a microSD card (at least 2GB), and and a microUSB power source (at least 2A).

Who came up with this solution?

MrEngman is the developer of this solution, and he’s regularly uploading new drivers as new kernels come out. The driver files are uploaded to his website, and the file’s naming convention for the necessary kernel is explained here in the corresponding Raspberry Pi forum post.

What do I need to do before I install the driver?

Burn the latest Raspbian Lite image on the microSD card, and before you boot it for the first time, create the wpa_supplicant.conf file on the boot partition. This wpa_supplicant.conf contains all the settings and credentials which allow the Pi to connect to your WiFi router. This will be important at the end of the tutorial, but we do it now to take care of it.

In Raspbian Stretch you need these lines in wpa_supplicant.conf Explained here in the Raspberry Pi Forums.

I use the below wpa_supplicant.conf setup:

ctrl_interface=DIR=/var/run/wpa_supplicant GROUP=netdev
update_config=1
country=US

network={
	ssid="Haper"
	psk="hellohello"
	key_mgmt=WPA-PSK
}

After the wpa_supplicant.conf is created, put the microSD card into the Pi Zero, then give it power to boot up.

How to install the RTL8188eu driver

First we need to determine the kernel version, which will be used to download the proper version of the 8188eu driver. The version and the number will be important in the next step.

Log in using the display and USB keyboard (pi/raspberry), and type this command to determine the kernel version.

uname -a

Output:

Linux raspberrypi 4.9.29+ #1000 ...

Note the kernel version.

After this you can shutdown the Pi again with

sudo shutdown now

and put the microSD card back in your computer.

On your computer you need to download the driver file. The filename you need to download is determined by the kernel version.

As an example for the Raspbian kernel 4.9.29(-v7)+ #1000 and driver 8188eu:
Pi1/Pi0: 8188eu-4.9.29-1000.tar.gz

http://www.fars-robotics.net/8188eu-4.9.29-1000.tar.gz

Pi2B/Pi3B: 8188eu-4.9.29-v7-1000.tar.gz (note the hyphen and v7 in the file name)

http://www.fars-robotics.net/8188eu-4.9.29-v7-1000.tar.gz

After you downloaded the file, uncompress the archive, it should be a folder. Copy this folder to the /boot/ partition of the SD card (that’s the only partition which Windows sees).

The folder should contain 3 files:

8188eu.conf
8188eu.ko
install.sh

Safely remove the microSD card from your PC and insert it again to the Pi Zero. Boot it up.

Log in using the display and USB keyboard again, and look for the folder you’ve coped to the boot partition.

cd /boot/8188eu[press TAB]

In my case it was:

cd /boot/8188eu-4.9.29-1000/

You need to run the install.sh script to install the driver:
sudo ./install.sh

After the driver installation, run the raspi-config setup tool and set up the basic settings:

sudo raspi-config
1 Change User Password
2 Hostname
5 Interfacing Options > P2 SSH > Enable? 
7 Advanced Options > A1 Expand Filesystem
7 Advanced Options > A3 Memory Split > 16


Reboot now? 

Log in again using your display and USB keyboard, and type this:

watch -n 5 ifconfig

Then, unplug your USB keyboard from the USB-OTG adapter, and plug in the RTL8188eu WiFI dongle.

When you plug in the dongle, apart from the loopback interface the wlan0 interface should appear. If you’ve configured the WiFi SSID and password correctly in the wpa_supplicant.conf file, it will try to connect to your WiFi router automatically, and if your router is set up to provide IPs via DHCP, the IP address of your Pi should be visible here after a minute or so. You can exit this with Ctrl+C.

Since the SSH server should now be running, you can use an SSH client on your PC to connect to your Pi.

Success? You have reached the Pi Zero via Wifi!

This tutorial has been revised on: 2017-Oct-10
Tested on OS image: 2017-09-07-raspbian-stretch-lite.img