There are two honest ways to make a PNG smaller, and it helps to know which one you are asking for. A lossless re-pack rearranges the file without altering the image; it is safe and it is modest. Palette reduction lowers the number of distinct colours stored, which is where the dramatic savings live.
Pick a strength below and the tool applies it. If you would rather do this in software you already have, the guides cover Preview, Photos, Photoshop, GIMP and Paint.
What the settings actually do
None re-encodes the file with maximum effort and strips metadata, leaving the pixels untouched. Expect 5–15%.
Gentle, Standard and Aggressive map the image onto 256, 128 and 64 colours respectively, chosen adaptively from the colours actually present. Flat-colour artwork survives this almost perfectly, because it never had thousands of distinct colours to begin with. Smooth gradients are where banding appears first, so step down gently if your image has large soft transitions.
When compression is the wrong question
If the image is a photograph, no PNG setting will compete with simply storing it as WebP or JPEG. If the image is displayed at 800 pixels wide but stored at 4000, the dimensions are the problem, not the encoding — see large PNG handling. Reach for the compressor once the format and the dimensions are already sensible.