1. Always use control centre to enable Personal Hotspot
We know, you can turn it on from Settings > Personal Hotspot too, but that approach can hide the cause of your problem.
When you enable Personal Hotspot from the Settings > Personal Hotspot panel, the icon will turn green and it'll look like it's turned on. However, if you have Wi-Fi turned off on your phone there's no error or any other visible sign that Hotspot isn't actually enabled at all.
Opening Control Centre
Swipe up from the bottom of the screen to open Control Centre if you're on an iPhone that has a home button (iPhone 5s, 6, 7, 8) - or swipe down from the right side of the screen if you don't have a home button (iPhone X, XS, XR).
Then tap and hold on the network stack (top left corner) until you see all six icons above.
2. Check the state of the Wi-Fi button
The Wi-Fi button should be either white (indicating that the Wi-Fi hardware is enabled, but it's not trying to join any nearby Wi-Fi networks) or blue which means it's either connected to a Wi-Fi network, or is searching for one.
If the button is transparent like the image on the right and it says "Off" below the button, you need to tap the Wi-Fi button to turn it on.
3. Enable Personal Hotspot
Tap the Personal Hotspot button. It will turn green and show "Discoverable" until the terminal connects, when that will change to "1 Connection".