In this paper we survey methods by which supersymmetry (or other new physics) could be observed in experiments at present and future
accelerators. We review some of the motivation for supposing supersymmetry might be a symmetry of nature even though there is presently no evidence for it. We try to systematize the necessary new notation, and discuss in some detail how to calculate results, with considerable emphasis on
pedagogical completeness. We summarize present limits on the existence of supersymmetric partners of ordinary particles, and show how to get improved quantitative limits if supersymmetric particles are not detected, so that eventually it is possible to be sure they are either detected or do not exist on the mass scale accessible to experiments.