There is a huge amount of technique and material to know if you want to do high quality color halftone separations, but if you can stand a method that should only take you 30 seconds, but will at least get you close to the example you posted, just do the following:
1. Load your original into PS.
2. Go to the "channels" palette, and nudge each of the three RGB channels by a few pixels, each in a different direction. This gives you color fringes like those in the example you posted.
3. Go to filters / color separations and experiment with all the parameters.
The attached files shows the above steps, starting with the original artwork.
It's certainly not exact (eg, the dots are too coarse, I used too many colors and the wrong ones, etc.), but it should give you some ideas on how to proceed.
HTH,
Tom M