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Cluster randomized trials (CRTs) are commonly used to evaluate the causal effects of educational interventions, where the entire clusters (e.g., schools) are randomly assigned to treatment or control conditions. This study introduces statistical methods for designing and analyzing two-level (e.g., students nested within schools) and three-level (e.g., students nested within classrooms nested within schools) CRTs. Specifically, we utilize hierarchical linear models (HLMs) to account for the dependency of the intervention participants within the same clusters, estimating the average treatment effects (ATEs) of educational interventions and other effects of interest (e.g., moderator and mediator effects). We demonstrate methods and tools for sample size planning and statistical power analysis. Additionally, we discuss common challenges and potential solutions in the design and analysis phases, including the effects of omitting one level of clustering, non-compliance, threats to external validity, and cost-effectiveness of the intervention. We conclude with some practical suggestions for CRT design and analysis, along with recommendations for further readings.