First, you need to understand the difference between Find My and Find My network; they're two connected but separate features. Find My is the app you use to locate your phone, while the Find My network is the crowdsourced Bluetooth system you must enable in order to find your iPhone even if it's offline. And this might not be on by default.
To check these options, go to Settings on your iPhone and select your name at the top. Choose Find My > Find My iPhone, then make sure Find My iPhone and Find My network are both enabled. The first slider is the core functionality, while the second explains that it lets you locate your phone even when it's offline, in Power Reserve mode or turned off.
Under that option is Send Last Location, which you should also turn on if it isn't already. It's a safeguard that has your iPhone sends its location to Apple one last time as soon as the battery reaches a critically low status. Speaking of which, Location Services (Settings > Privacy & Security > Location Services) and Bluetooth (Settings > Bluetooth) need to be enabled, and the iPhone needs to have sent its location to Find My within the last seven days to locate it.
To verify everything is working, swipe down from the top-right of the screen and hold the Power icon in the top-right corner. The power-off screen will pop up, where you should see iPhone Findable After Power Off noted underneath the slider.
If someone steals your phone, they'll likely try to take it offline so it's harder to track. To prevent this, go to Settings > Face ID & Passcode and scroll down to the Allow Access When Locked section. Here, disable Control Center so thieves can't put your phone in airplane mode. They can still turn it off, but that's better than it being disconnected. It's safe to leave Siri enabled, since Siri will ask you to unlock your phone before sensitive actions like enabling airplane mode.