A D3.js smiley face is drawn with SVG shapes: a yellow circle for the head, two circles for eyes, rectangles for eyebrows, and a curved path for a mouth. The face is centered on an SVG canvas, and animated eyebrows and mouth move through a sequence of positions using D3 transitions with a two-second duration. The code explicitly uses D3's `select`, `append`, `attr`, and `transition` methods to manipulate DOM elements, building the face from primitive shapes.