Quote Originally Posted by mfratt View Post
How do I determine the correct shutter speed?
Though, as was mentioned, the flash's duration will be the shutterspeed for the flash exposure, you do have to check the ambient light levels, and make sure that the aperture-shutterspeed combinbation you set will render the bits exposed by ambient light the way you like them to be. (Because, opposed to what was suggested, ambient light levels do come into play even when not very bright.)

So it's a double job: both flash and ambient light exposures have to be checked and regulated.
You set the aperture to get the correct flash exposure, and use the shutterspeed to control the balance between flash and ambient light exposures.