There is nothing magical about fill-flash. You just have to recognise when you are in a situation that needs it. Then it is just a matter of flipping up the built-in flash and proceeding as normal. Provided you have the fill-flash setting enabled, it will come into operation automatically when you raise the pop-up flash and your DSLR will (usually) do the right thing without your needing to worry too much about it.
A situation that calls for fill-flash is one where you want to use natural light but the light is coming from behind the subject, causing the subject to come out too dark. With fill-flash operating, the background will still be lit by natural light, and the automatic exposure will be set accordingly, but the flash will also fire so that the combination of natural light and flash will result in the subject being properly exposed too.
An example from my recent cruise. Naomi was dressed up for the gala night and we went out onto our cabin’s balcony, which was facing out from the back of the ship, to see the sunset. I realised that by using fill-flash I could capture both Naomi and the sunset, with both correctly exposed. It does not always work perfectly but on this occasion I was very pleased with the result, aside from the fact that the horizon could have been straighter.
The reason fill-flash sometimes does not work properly has to do with the flash sync shutter speed. Assuming you are using Aperture Priority, as many photographers prefer to, the camera will set the shutter speed to expose the background correctly. But if the background is reasonably bright and the chosen aperture is too wide then the shutter speed needed to expose the background correctly could well be higher than the camera’s shutter sync speed. If the flash were to fire in conjunction with a high shutter speed the shutter would never be fully open and only a part of the subject (a strip) would be illuminated by the flash. Trying to use fill-flash in those circumstances would force the camera to reduce the shutter speed to the sync speed and probably overexpose the entire image.