Disconnect Bluetooth Devices
For some reason, when you have a Bluetooth device connected to your iPhone (other than your Apple Watch), Siri just doesn't seem to work at all.
Usually, it will activate just fine from holding down the Home button, but it won't recognize anything you say. This seems to be a bug that hopefully Apple fixes, but it's also likely that Siri may think that the Bluetooth device connected to your iPhone has a microphone of its own, even when it doesn't. So it will use this non-existent microphone instead of your iPhone's microphone.
Many Bluetooth speakers have built-in microphones, and Siri can detect this and use that microphone for Siri automatically. However, I think Siri may not know that other Bluetooth devices don't have their own microphone, but will try to use it anyway, resulting in the bug that users have been experiencing.
Because of this, it's probably best to disconnect any Bluetooth devices from your iPhone if you're wanting to use Siri for the time being.