What is this style called? I want to recreate this effect on a photo myself. Also, does anyone have tips on how to accomplish this?
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That’s a halftone.
It can be achieved in Photoshop by choosing
Filter → Pixelate → Color Halftone.
The example you posted looks like the halftone version of the image has been blended with the original.
In GNU Image Manipulation Program (GIMP), you can halftone a photo with Filters > Distorts > Newsprint. On deviantART, istarlome provided a tutorial for halftoning in GIMP. Here's the gist: