The iPhone does not need to be placed into pairing mode. It will automatically discover a headset that is in pairing mode.
Once the headset is in pairing mode, your iPhone should "discover" it. On the Bluetooth settings screen, you'll see the name of the headset appear under the list of devices. Simply tap the name of the headset, and the iPhone will connect to it. For Leitner, it will say "DECT Headset", as an example.
You may be asked to enter a PIN; if so, the headset manufacturer should supply the number you need. Once the correct PIN has been entered, the iPhone and the Bluetooth headset are paired.
Time for a new headset?
Many iPhone users have made the switch to the Leitner LH370!