Adaptive quadrature is a numerical integration technique which is emerging as a fundamental part of approximate Bayesian inference algorithms, providing a computationally attractive and user-friendly alternative to MCMC for a wide class of problems. However, unlike MCMC which is fully general and taught at the graduate or senior undergraduate level as part of a typical statistics curriculum, applications of approximate Bayesian inference using adaptive quadrature are currently effectively limited to existing software packages and the models coded into them. I overview recent advances in approximate Bayesian inference and then introduce the aghq R package and show how it can be used by a statistical audience to fit complicated models from scratch. I demonstrate this approach using models for the spread of infectious diseases, estimating the mass of the Milky Way, and mapping spatial variation in disease risk with zero-inflated count data. Interested audience members with a background in statistics could leave this presentation able to implement approximate Bayesian inference from scratch for their models and data.