Tested with Kali 2018.2

• Update the system:

  apt-get update
  apt-get upgrade
  apt-get dist-upgrade

• Reboot:

  reboot

• Install the required packages:

  apt-get install git build-essential

• Install the driver, if something went wrong earlier, and you want to try again, add --reinstall:

  Make sure the following line is in /etc/apt/sources.list
  deb http://http.kali.org/kali kali-rolling main contrib non-free
  
  apt install realtek-rtl88xxau-dkms

• Reconnect the device. The journal will show the following messages:

  Jun 03 12:07:02 kali kernel: usb 2-1.3: New USB device found, idVendor=0bda, idProduct=8812
  Jun 03 12:07:02 kali kernel: usb 2-1.3: New USB device strings: Mfr=1, Product=2, SerialNumber=3
  Jun 03 12:07:02 kali kernel: usb 2-1.3: Product: 802.11n NIC
  Jun 03 12:07:02 kali kernel: usb 2-1.3: Manufacturer: Realtek
  Jun 03 12:07:02 kali kernel: usb 2-1.3: SerialNumber: 123456
  Jun 03 12:07:02 kali mtp-probe[5364]: checking bus 2, device 5: "/sys/devices/pci0000:00/0000:00:06.0/usb2/2-1/2-1.3"
  Jun 03 12:07:02 kali mtp-probe[5364]: bus: 2, device: 5 was not an MTP device
  Jun 03 12:07:02 kali kernel: 8812au: loading out-of-tree module taints kernel.
  Jun 03 12:07:02 kali kernel: RTL871X: module init start
  Jun 03 12:07:02 kali kernel: RTL871X: 8812au v4.3.21_17997.20160531
  Jun 03 12:07:02 kali kernel: RTL871X: build time: Jun  3 2017 12:02:43

• Check rfkill:

  rfkill list / block

• Stop NetworkManger from interfering:

  systemctl stop NetworkManager
  airmon-ng check kill 

• Enable monitoring:

  airodump-ng start wlan1

• Start monitoring:

  airodump-ng --band abg wlan1