Why?

Unlike Ubuntu desktop, Ubuntu server does not come with NetworkManager. This is one way (without installing NetworkManager) to get WiFi working on Ubuntu server.

Install packages

First, install the packages that we will need. Strictly speaking, wireless-tools isn't necessary, but it's nice to get iwconfig.

sudo apt install wireless-tools
sudo apt install wpasupplicant

Now, figure out the name of your wireless adapter:

$ iwconfig
wlx60somelongstring  IEEE 802.11bgn  ESSID:off/any
          Mode:Managed  Access Point: Not-Associated   Tx-Power=20 dBm
          Retry short limit:7   RTS thr:off   Fragment thr:off
          Power Management:off

...

Next, add a configuration for your wireless adapter to /etc/network/interfaces:

# Wifi
auto wlx60somelongstring
iface wlx60somelongstring inet dhcp
wpa-ssid <your SSID>
wpa-psk <your WiFi Password>

Finally, restart networking via systemd:

sudo service networking restart

At this point your wireless adapter should automatically connect to your AP. Also, because we put auto in /etc/network/interfaces, it should come up on every boot.

iwconfig

At this point, if desired, you can use iwconfig to inspect the connection:

$ iwconfig
wlx60somelongstring  IEEE 802.11bgn  ESSID:"<your SSID>"
          Mode:Managed  Frequency:2.437 GHz  Access Point: XX:YY:ZZ:AA:BB:CC
          Bit Rate=72.2 Mb/s   Tx-Power=20 dBm
          Retry short limit:7   RTS thr:off   Fragment thr:off
          Power Management:off
          Link Quality=67/70  Signal level=-43 dBm
          Rx invalid nwid:0  Rx invalid crypt:0  Rx invalid frag:0
          Tx excessive retries:30  Invalid misc:17   Missed beacon:0

...