We present a pedagogical introduction to NRQED (non-relativistic quantum electrodynamics). NRQED is an effective field theory that describes the interaction of non-relativistic, possibly composite, spin-half particle with the electromagnetic field. We explain in detail how the NRQED Lagrangian is constructed up to and including order 1/M
2, where M is the mass of the spin-half particle. As a sample application, we derive the Thomson scattering cross section for the low energy scattering of a photon and a possibly composite spin-half particle.