Stein’s method for distributional approximation was originally developed in the context of normal approximation. It is appropriate for use with network statistics, such as subgraph counts, when the typical counts are large; (compound) Poisson approximation is most useful in sparse networks, normal approximation when networks are denser. In this chapter, Stein’s method for estimating the error in normal approximation, measured with respect to the bounded Wasserstein distance, is outlined. A Stein equation, a first-order ordinary differential equation is derived, and some properties of its solutions are established. Direct application of these results leads to a general bound on the approximation error, which is then applied in the classical context of sums of independent random variables. Then, both local and size bias coupling approaches are developed. The local approach, which uses a double decomposition, is illustrated by application to the number of triangles in the Bernoulli random graph; the calculations are typically more involved than for Poisson approximation. The coupling approach is applied to the distribution of the sample mean in simple random sampling.