Longitudinal data sources offer new opportunities for the evaluation of sequential interventions. To adjust for time-dependent confounding in these settings, longitudinal targeted maximum likelihood based estimation (TMLE), a doubly robust method that can be coupled with machine learning, has been proposed. This paper provides a tutorial in applying longitudinal TMLE, in contrast to inverse probability of treatment weighting and g-computation based on iterative conditional expectations. We apply these methods to estimate the causal effect of nutritional interventions on clinical outcomes among critically ill children in a United Kingdom study (Control of Hyperglycemia in Paediatric Intensive Care, 2008-2011). We estimate the probability of a child's being discharged alive from the pediatric intensive care unit by a given day, under a range of static and dynamic feeding regimes. We find that before adjustment, patients who follow the static regime "never feed" are discharged by the end of the fifth day with a probability of 0.88 (95% confidence interval: 0.87, 0.90), while for the patients who follow the regime "feed from day 3," the probability of discharge is 0.64 (95% confidence interval: 0.62, 0.66). After adjustment for time-dependent confounding, most of this difference disappears, and the statistical methods produce similar results. TMLE offers a flexible estimation approach; hence, we provide practical guidance on implementation to encourage its wider use.