In order to make quantitative predictions for jet cross sections in perturbative QCD, it is essential to calculate them to next-to-leading accuracy. This has traditionally been an extremely laborious process. Using a new formalism, imaginatively called the dipole formalism, we are able to construct a completely general algorithm for next-to-leading order calculations of arbitrary jet quantities in arbitrary processes. In this paper we present the basic ideas behind the algorithm and illustrate them with a simple example.