With my hand held light meter I'd figure out what shutter and aperture settings get me the background exposure I wanted, and then I'd meter the flash, and adjust flash power or flash distance to control that exposure. With a simple flash it may be necessary to control flash power with aperture, but most modern flashes offer variable power settings. I'm trying to retain aperture choice to control DOF.
Without a meter I would use the sunny 16 rule (or Fred Parker's Ultimate Exposure Computer
http://www.fredparker.com/ultexp1.htm ) to figure ambient exposure, and flash guide number divided by distance to subject for flash exposure.
The above methods take a minute or so to figure. I used both when I shot film. Once figured it should remain the same unless the lighting changes, or the flash to subject distance changes.
Now that I shoot digital I quickly guestimate the exposure, take a test shot, check the histogram, and adjust. Repeat as necessary, although I can usually dial in the exposure I want in a matter of seconds. I like trial and error. It works for me. My math skills are deteriorating, but I'm using that brain power to interact with my subject and consider the scene, and I've found it results in better photos.