Hi Simon,
If I understand correctly, this photo booth is of the light-tent variety? I.e. a 5-sided cube-like shape, with the 6th face open for the camera?
These are usually used to get shadowless photos on a pure white background, for product photography, etc. They are particularly useful for very shiny things, like jewellery, as they will have less distracting things in the reflections.
The light source in your photos looks like it is coming through the opening that is used for the camera. This way, it is not being diffused by the white material of the tent.
Do you use a tripod? Without one, things are a bit more limited, so improvise with a pile of books or similar. Basically you want to remove the influence of camera movement and free yourself to use as long an exposure as needed. If you are using an improvise camera support, you will probably have to use the self timer so that your hand pressing the shutter does not vibrate the camera during the exposure.
First, set the ISO to be fixed at it's lowest setting, and disable any on-board flash. If you camera has a long enough exposure capability (2 seconds or so), you can start without any additional lighting (just the room lights, or preferably daylight from a window). This way, the white fabric of the tent should be the brightest thing in the frame, and you can adjust the exposure with the exposure compensation (usually labelled in EV steps) until it is a clean white background. If the camera is using its slowest shutter speed already, it may look too dark as it can't do anything to get more light in. In that case, you'll have to use extra lights. Start with the light above the tent, and positioned so that none comes straight in through the front opening of the tent. The light should bounce around inside the tent and give subtle shadows, they shouldn't look as dark as in the photos you have posted.
After you have mastered the single light above, you can add other lights (try to keep them the same light temperature- i.e. colour, so all halogens, all normal tungsten bulbs, all the same type of fluorescence lamp, etc.)- but again avoid any direct lighting. If you want light to come in from the front, drape a white cloth (or kitchen roll, anything to diffuse the light) over the opening, leaving just enough room for the camera, and place the light so that is has to pass through the diffuser before entering the tent.
Good luck, and let us know how you get on.