A didactic and systematic derivation of Noether point symmetries and conserved currents is put
forward in special relativistic field theories, without a priori assumptions about the
transformation laws. Given the Lagrangian density, the invariance condition develops as a set of
partial differential equations determining the symmetry transformation. The solution is provided in
the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields.
Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated
with the linear superposition of solutions, whenever applicable. The role of gauge invariance is
emphasized. The case of the charged scalar particle under external electromagnetic fields is
considered, and the accompanying Noether point symmetries determined. Noether point symmetries for a
dynamical system in extended gravity cosmology are also deduced.