In phonetics, many datasets are encountered which deal with dynamic data collected over time. Examples include diphthongal formant trajectories and articulator trajectories observed using electromagnetic articulography. Traditional approaches for analyzing this type of data generally aggregate data over a certain timespan, or only include measurements at a fixed time point (e.g., formant measurements at the midpoint of a vowel). This paper discusses generalized additive modeling, a non-linear regression method which does not require aggregation or the pre-selection of a fixed time point. Instead, the method is able to identify general patterns over dynamically varying data, while simultaneously accounting for subject and item-related variability. An advantage of this approach is that patterns may be discovered which are hidden when data is aggregated or when a single time point is selected. A corresponding disadvantage is that these analyses are generally more time consuming and complex. This tutorial aims to overcome this disadvantage by providing a hands-on introduction to generalized additive modeling using articulatory trajectories from L1 and L2 speakers of English within the freely available R environment. All data and R code is made available to reproduce the analysis presented in this paper.