As you know, in photography, fill lighting is simply used to fill in shadows. A good starting point for the fill light should be at around half the brightness of the main light, and adjusted to suit the effect you are going for. You generally want the fill light to be perpendicular to the main light, but obviously this is not always desirable. You also want the fill light to be as soft as possible, as its function is not to create shadows, but hide them.
There are many ways to use and place the fill. I like to use cheap white cardboard reflectors which you can buy from art shops for a few dollars, as these give a nice soft fill, and are easily bendable foam core is another option, but I prefer cardboard. This works particularly well for beauty lighting where the white cardboard is placed under the models face and bent upwards from either the front or the sides. This also gives a nice lower catch light as it is reflected in the eyes. You can adjust the intensity of the fill light by simply moving the cardboard further or closer to the subject. You want the fill light to be as soft as possible, which is why it’s best to use white over silver reflectors (although silver is sometimes more suitable).
Another method I sometimes use for fill is to bounce a strobe off a wall or the ceiling. essentially turning the surface into a giant soft box. This will give you a very soft light.
In this photo, I used the above method for the main light as I wanted the light to be very soft and even. I placed the strobe behind the camera and to the left and pointed it up to the ceiling. You will notice the light is still darker on one side of her face, but the effect is very subtle. I also placed two large rectangular soft boxes behind the model off to either side for some accent lights.