A smiling face is drawn with a yellow circle for the head, black-outlined, and two smaller circles as eyes. The smile is created using a D3 arc path with a specified inner and outer radius, rendered as an SVG path. The code defines the face elements with React, using SVG shapes like circles, a path, and rectangles for teeth. The example demonstrates how to integrate D3's arc generator for creating a mouth shape within a React-based SVG visualization. Names for the D3 API include `arc` and its chained methods for radius and angle specifications.