Here's a very thorough article from The New York Times. If you're not a subscriber, try and find another way to open it.

Tracker Detect that Apple has released for both its devices and Android devices that will scan for AirTags in range and let the users know of their existence. For some of the other devices you can also get other apps that will pick up the signals and at least warn you about some devices existence (not sure how good they are a pin-pointing the location)

I don't understand how these things work. How is connectivity provided? I know they use Bluetooth, but how do they connect to mobile devices without getting permission to do so?

That's BS. So these things connect with people's phones without them knowing it and without their permission. Another reason I don't use Apple products.

It's also how they do car jackings.  I'd research if you own hot cars on the market.  

Before driving out open your smartphone and turn on your bluetooth.  Check for local devices.  If there is an AirTag near you it will show up on your smartphone.