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What is a guide number (GN)?
One could define the power of flash (the energy of emited light) using one of the official, scientific units but this wouldn't be helpfull for photographers, therefore there is easy to use unit called flash guide number (GN). In short guide number is distance to object that should be properly exposed multiplied by aperture set on the lens.If one knows what the GN of flash is and knows the distance to photographed object it is only the matter of simple mathematics to calculate the right aperture. Notice that time does not matter as the flash is usually extremely fast, from 1/500th of a second up to 1/10000th of a second, therefore set the shutter speed to the shortest time that still synchronise shutter with the flash (called the X time), to avoide influence of ambient light.
Using GN
Looks nice but it is not that easy. First of all nearly all GN are calculated for ISO 100 sensitivity so if other camera settings (film sensitivity) is used GN needs to be recalculated. Multiply guide number by 1.41 for every full f-stop above ISO 100 or by 0.71 for every full f-stop below ISO 100. For example a 20 GN (for ISO 100) would be 28 GN for ISO 200 (20 ⋅ 1.41 = 28.2), about 40 for ISO 400 (20 ⋅ 1.4 ⋅ 1.4 = 39.8) and about 14 GN for ISO 50 (20 ⋅ 0.71 = 14.2).This is still not all. Guide number is measured using flash that is attached to a camera and pointed directly at the photographed object so when the flash is used off the camera one needs to use the distance from flash to photographed object, not from camera to photographed object. If flash and object are not moving the camera may change the distance and exposure will be exactly the same (if the shot is taken from the same side of object of course).
Flashing the ceiling or wall is even more complicated. The distance will be calculated as distance from flash to the middle of flashed part of the ceiling (wall) + distance from that point to the photographed object (in other words if we are bouncing flash from the ceiling that is 2m above us at 45 degree angle, the distance is two times 2.8m what gives 5.6 meters - remember the geometry classes!). This is not all. Every surface that reflects light absorb some of it. Mirrors absorb about 5% of the light but white wall about 50% (1 EV), therefore one needs to open the aperture by extra 1 EV in this case. Of course the method I presented hee is not 100% accurate. It is a good start in typical conditions (white ceiling, flash at 45 degree).
Flash is not always used as primary light source. Quite often it is used only to brighten the shadows (so caled fill flash). In this case photographer needs to make the flash weaker or the image will be blown out. For fill flash calculate the right aperture using GN and then close it about 2 EV (or choose 1/4 of the correct power of the flash).
Controlling the light
Photographer needs to take full control over the light therefore, in flash photography, over the power of flash. In modern flash systems there is TTL metering and one needs only to know how to compensate the flash to get the right results. Unfortunately in cheap, home studio I have only one, manual flash (constant 20 GN). If you are looking for cheap photography, or want to have total control in your studio you need to use GN and few tricks. If you need to make your manual flash "weaker", and there is no option to set the power on it you can wrap the flash with something to absorb some of the light. I found that splitting a tissue into the thinnest layers is a good idea. Every of the paper layer absorbed about 1EV. That was very usefull when I had to shoot macro in my sudio and the flash was really near the object.There is another piece in this puzzle - diffusing the light to make it softer. Let's start from the beginning: what does "soft" and "hard" light really mean? Hard light is emited by one, small (or distant) object, therefore all the shadows have very hard (sharp) edges (bright sun, bulb, direct flash). Soft light is emited by a big and not so distant surface in all directions, therefore every object is lightened from many different directions making the shadows brighter with soft edge. Thst's why all softboxes and diffusers must be close to the photographed object and as big as possible. Light reflected by wall or ceiling is soft, as well as sunlight during cloudy day. The big question is - how to make hard light from flash soft? First try to bounce the flash. Unfortunately it is not always possible (ceiling too high, colorfull, shooting outdoor far from walls, building or big rocks). Another idea is to use big piece of semitransparent plexi or foil and place it between the flash and photographed object. Usually the stronger the effect the more light is absorbed by diffusing material - sorry.