How should I position a single umbrella flash for a photobooth?

Generally speaking for 'photobooth' style photography the number one priority is for a lighting setup that will work for every single person who sits in front of the camera without having to fiddle with the lighting at all for the entire time the photobooth is set up. Not having to monkey with lighting is what allows the camera operator to get as many people in and out as fast as possible with very predictable and uniform results.

It is actually a relatively easy thing to to do with a single light source... Simply place the light directly behind and above the photographer pointing right at the subject adjust the light's power once at the beginning of the evening to get a reasonable balance, and you shouldn't have to adjust it again. This will produce a flat light that is not especially interesting (or all that great looking) but it will tend to give a bit of sparkle to the eyes, and most importantly will light people's faces in a uniform way and will eliminate any harsh shadows from the subject.

Companies that provide these types of photographs (santa pictures, yearbook photos, prom pictures, photobooths, etc.) often refer to this as 'yearbook portrait' lighting (as well as other much more derogatory terms), but its value to these companies is that it's less of a 'lighting style' and more a method of lighting that produces 'adequate results and can be taught to a minimum-wage camera operator in a 2-hour training session'...