To use a Bluetooth Mouse, your iPad must be updated to iPadOS 13.2 or later.
If you have fourth generation iPad, as outlined in the subject line of your post, your iPad cannot be updated beyond iOS 10.3.3 (WiFi only) or iOS 10.3.4 (WiFi+Cellular). As such, a Bluetooth mouse is not supported by your iPad.
For other iPad devices that can be updated to iPadOS 13.2 or later, the iPad User Guide outlines the process of pairing Bluetooth accessories - such as a compatible keyboard, mouse or trackpad - with your iPad:
Set up and use Bluetooth accessories on iPad - Apple Support
You should also refer to the pairing procedure for specific third-party accessory - which will be found within its associated User Guide.
As for compatible mice, basic three-button + scroll mouse functions are supported by iPadOS. Any additional functions that nominally require installation of driver software are not supported by iPad. The only method of installing device-specific drivers is through installation of a device-specific App, provided by the device manufacturer, from the App Store.