The Pi-Hole URI is the beginning of whatever you use to connect to the Pi-Hole web interface. For example if you enter:
http://192.168.1.200:8181/admin
to access the web interface, you should enter:
http://192.168.1.200:8181 into PiContrHOLE.
Ensure you're entering the correct protocol (HTTP/HTTPS) and (if necessary) ports.
You can test the API by visiting:
http://YOUR_PI_IP/admin/api.php?summary
If you see data on the screen, your pi-hole is setup correctly.
If the page does not load, please first fix the configuration of your pi-hole and check your firewall settings.
Note that if you are accessing your pi-hole outside of your local network, you must communicate over HTTPS (An iOS rule).
One of the simplest ways to acquire the API Key is to, in the pi-hole webapp copy the key from:
Settings > API/Web Interface > Show API Token
If that doesn't work, alternatively (and i've found more reliably), you can connect to your pi-hole over SSH (or physically), navigate to the:
/etc/pihole/setupVars.conf file, and copy the WEBPASSWORD entry.
Enter just the part after the WEBPASSWORD=