  We provide a comprehensive discussion, together with a complete setup for
simulations, relevant for the production of a single vector-like quark at
hadron colliders. Our predictions include finite width effects,
signal-background interference effects and next-to-leading order QCD
corrections. We explicitly apply the framework to study the single production
of a vector-like quark $T$ with charge 2/3, but the same procedure can be used
to analyse the single production of vector-like quarks with charge $-4/3$,
$-1/3$, $2/3$ and $5/3$, when the vector-like quark interacts with the Standard
Model quarks and electroweak bosons. Moreover, this procedure can be
straightforwardly extended to include additional interactions with exotic
particles. We provide quantitative results for representative benchmark
scenarios characterised by the $T$ mass and width, and we determine the role of
the interference terms for a range of masses and widths of phenomenological
significance. We additionally describe in detail, both analytically and
numerically, a striking feature in the invariant mass distribution appearing
only in the $T \to th$ channel.
