Lattice regularization of quantum field theories (lattice QFT) is a powerful tool for understanding such theories when analytic methods are not applicable. However, the utility of numerical results can be affected by two issues: (i) calculations are necessarily performed in a finite-volume spacetime, and (ii) imaginary-time correlation functions are estimated. Both aspects play a particularly important role for multiparticle observables, including scattering and decay amplitudes. In these lectures we will give an overview, together with various detailed examples, on the topic of extracting scattering amplitudes using numerical lattice field theory. We will focus on the strategy of using the finite volume as a tool rather than an unwanted artifact, and of applying generic field-theoretic relations between finite-volume quantities and infinite-volume amplitudes. Specific topics include the challenges of two-to-three and three-to-three amplitudes and the role of anomalous thresholds. The lectures will include an overview of how the relations are derived and their limitations, as well as a small (and biased) selection of numerical results.