A tutorial on the modern definition and application of moving frames, with a variety of examples and exercises, is given. We show three types of invariants; differential, joint, and integral, and the running example is the linear action of $SL(2)$ on smooth surfaces, on sets of points in the plane, and path integrals over curves in the plane. We also give details of moving frames for the group of rotations and translations acting on smooth curves, and on discrete sets of points, in the conformal geometric algebra.