yep, i do refer to the built-in flash.
Unfortunately, I have not used the H1. However, it probably works similar to most digital slr cameras. I find that I have the best control is with manual. However, here is a guess about using the H1.... :-)
Assume you wish to have the flash unit dominate the light and not be a simple fill flash. Also assume you are in aperture priority and have your camera set to F5.6. If the shutter speed is reasonable in the ambient light (maybe 1/25 second or faster), set up the camera to under-expose by one stop by adjusting the exposure compensation system. This would result in an under-exposed image at 1/50 second at F5.6 without flash. Now enable the flash - tell the flash (I assume on a setup menu for the camera) that you wish to have NORMAL flash exposure.
If you shoot the image, the camera will under expose by one stop as you directed. However, the flash will sense the under-exposure and give your stronger fill. In this case, there will be one stop more light from the flash than from the ambient light.
An alternative is to use manual exposure (maybe by light meter) and set the camera for a one stop under-exposure. If you fire the flash, the flash system will compensate and give you a proper exposure - again, it will be one stop stronger than the ambient light.
Hope the above applies to the H1 :-)