I run a photobooth for a friend at a party for a side job and last night we came across a predicament. We only were able to use one flash on a tripod, instead of the usual two, along with the camera flash that has a Gary Fong on it. I couldn't seem to get rid of some dark shadows under people's arms and ears/hair.
What would be the best placement for the umbrella flash when I come across this again?
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'...
If you have some resources on hand for creating a reflector of some sort, you can go with a butterfly using the strobe and the reflector. Pretty much any basic white board of some sort will do the trick assuming you can get the light high on the subject. DIY Photography has a pretty good article on the technique showing a diagram and some outcomes as well as Jay has one here with much prettier diagrams. :)
Now, if you can't take the strobe off the camera but you can tilt/rotate it, then you can try to make it a bigger light source. One approach to this, again with the makeshift reflector is to direct the light to the side and onto the reflector that is then aimed at the subject. This will soften the light and make it bigger, creating softer shadows. A second reflector may be useful, if you can, to fill in the other side, further reducing and softening the shadows.
As a side note, the reflectors can be bristol board or something along that line, they do not have to be expensive, professional, options.
Rembrandt Lighting (high and to one side) is a one-light setup. It's probably the most common and useful one.
Get the umbrella as close as possible (while still being out-of-frame) to avoid hard shadows.
Depending on exactly where the dark shadows are, you might be able to increase the power of your on-camera flash (ie: your fill light) relative to your main flash (ie: your key light).
However, if this is a one-time-setup fire-and-forget photobooth, you might not be able to get good shots every single time. People, bodies, poses, and positions will change every time. Manage your expectations accordingly.
One easy way to help eliminate those shadows, is the use of a relector, as mentioned in another answer. However, this usually means you need help. For an effective reflected fill, try a white floor cover, drop cloth, or even put sheets of white poster board on the floor. Usually there will be enough reflected fill to soften these shadows, and you don't need any help. This works especially well if the umbrella is above and behind the photographer, and facing the subject.
