  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.
