A common way to get this look is to posterize the photo: reduce it to just a few tonal/color areas, then clean it up and optionally vectorize it.

Typical workflow:

1. Start with a photo that already has strong contrast and simple lighting.
2. Reduce tones/colors using posterize, curves, or by converting to grayscale first and simplifying the tonal range.
3. Limit the image to a small palette (for example 3–5 colors) and adjust those colors manually.
4. If you want the true illustration/vector look, bring it into a vector app such as Illustrator, CorelDRAW, Affinity Designer, or Inkscape and vectorize/redraw the shapes.
5. Edit individual shapes/colors by hand for a cleaner result.

Important: this effect does not work equally well on every image. Photos with clear subject separation, bold contrast, and fewer colors work best. Random photos often need significant manual cleanup.

You may also find tutorials/plugins by searching for the “Obama Hope poster” style, since that popularized this kind of color-reduction treatment.