Disposable cameras usually work in a completely fixed mode of operation (lens focus, aperture and shutter speed). The flash can be turned on or off but power output is fixed . Exposure variations are handled during developing (since nobody expects the absolute highest quality from disposable cameras the effects of pushing or pulling the film go unnoticed).
Fuji disposables use a single element 30mm f/11 lens whilst the ones made by Kodak have a patented 30mm f/10 lens consisting of two aspherical moulded plastic elements. Both manufacturers use a shutter speed of 1/100s and ISO800 film.