D3.js constructs a smiling face from SVG shapes, including a yellow circle for the head, two eyes, and an arc-based mouth using the `d3.arc()` generator. The eyebrows, rendered as rectangles, animate vertically through chained `transition().duration()` calls, moving up and down over two seconds each. The code uses D3 selections and attributes to position elements around a centered group, with all coordinates based on the SVG’s 960×500 dimensions.