Doug Sillars discusses optimizing images for fast delivery on mobile websites. He outlines 4 simple optimizations: 1) reducing image quality, 2) using optimized formats like JPEG, PNG and WebP, 3) sizing images appropriately through responsive images, and 4) lazy loading images below the fold. Formats like SVG and GIFs can further reduce file sizes. Tools like ImageMagick and libraries like LazySizes can help automate optimizations to deliver fast and beautiful images.