If you are trying to film an event that just happens to be in the rain but you want to avoid it being too distracting in the final video, then you should avoid using too much unnatural light. Any strong beam of light will highlight each raindrop and it will appear as another texture or surface on the screen. If it is just too dark to use natural light make sure to use a small light going as straight from the camera as possible. A waterproof on-board light, or possibly a weak flashlight held directly above the camera, would work best for this.
If your intent is to capture the rain then it is important to light the rain strongly with a backlight. You can hang the light off to the right or left of the view of the camera, but try and make sure the light is set up more than ten feet away from the camera and tilted toward the lens of the camera. Think about the rain as the subject in an interview and use this light similar to how you would use a backlight to highlight the back of a person. If the rain is too heavy to use artificial light try and shoot towards where the natural light is coming. Check the time of day and if it is early in the day you shoot facing the east, and if it is in the later afternoon you should point the camera toward the west. That way the natural light will be coming right through the rain, acting as a diffused backlight.
So whether you are filming in the rain out of necessity, or on purpose, following a few simple guidelines can help you get the footage you are looking for.