We present a general method for incorporating the electromagnetic interaction into descriptions of hadronic processes based on four-dimensional scattering integral equations. The method involves the idea of gauging the scattering equations themselves, and results in electromagnetic amplitudes where an external photon is effectively coupled to every part of every strong interaction diagram in the model. Current conservation is therefore implemented in the theoretically correct fashion. To illustrate our gauging procedure we apply it to the three-nucleon problem whose strong interactions are described by standard three-body integral equations. In this way we obtain the expressions needed to calculate all possible electromagnetic processes of the three-nucleon system: the electromagnetic form factors of the three-body bound state, pd → pdγ, γ3He → pd, γ3He → ppn, etc. As the photon is coupled everywhere in the strong interaction model, a unified description of the NNN-γNNN system is obtained. An interesting aspect of our results is the natural appearance of a subtraction term needed to avoid the overcounting of diagrams.