We use the Guide Number as an aid to gauge the f-number setting.
Accept, as an example, your ISO setting is 200. You consult a table of guide numbers and discover it’s 180. Your principal subject is 10 feet downstream of the flash. What would be the appropriate f-number setting? To compute, we divide guide number by distance -- thus 150 ÷ 10 = 15.5. Now round to the nearest full f-stop = f/16.
In modern times, the shutter speed setting is moot because the source of the flash is an electrical discharge of high voltage applied to a glass tube filled with xenon gas. A super short blitz of light ensues. The blitz is so quick that few, if any shutters have any ability to mitigate. Thus the real problem is synchronization. Now we are talking the timing of the applied charge so that the shutter will be fully open when the blitz occurs. There are exceptions when using specialty high-speed cameras.
The published guide number is just a good guestimate. Several difficult to predict factors come into play. To name a few: Indoor or outdoor scene – height and color of indoor ceiling – reflectivity and contrast of scene - size and shape to flash reflector – plus many more.
To refine the guide number for an actual shoot: On scene, shoot a series at different f-stops. The idea is to discover a setup that delivers a faithful image. Pretend f/11 works. Now multiply the principle subject distance by f-stop used. Say 10 feet @ f/11 – revised guide number is 10 x 11 = 110.
Setting for synchro-sunlight: For flash fill in sunlight, likely best is flash subordinate to sunlight by 1 f-stop. We adjust flash-to-subject distance to achieve. Better method is to adjust flash power if possible. If not, set shutter speed to synchronize. Set camera f-number for sunlight exposure. Divide guide number by principal subject distance. Pretend f/11 with guide number of 120.
Now divide 120 by 11 = 11 (rounded ). This is distance in feet flash to principal subject. At this distance, flash intensity mirrors sunlight exposure. Now multiply this distance by 1.4 = 16 (rounded). This is flash to subject distance, one f-stop subordinate.