In the first step, the protein of interest (POI) is cross-linked with the DNA site it binds to in an in vitro environment. Usually this is done by a gentle formaldehyde fixation that is reversible with heat.
Then, the cells are lysed and the DNA is sheared by sonication or using micrococcal nuclease. This results in double-stranded chunks of DNA fragments, normally 1 kb or less in length. Those that were cross-linked to the POI form a POI-DNA complex.
In the next step, only these complexes are filtered out of the set of DNA fragments, using an antibody specific to the POI. The antibodies may be attached to a solid surface, may have a magnetic bead, or some other physical property that allows separation of cross-linked complexes and unbound fragments. This procedure is essentially an immunoprecipitation (IP) of the protein.  This can be done either by using a tagged protein with an antibody against the tag (ex. FLAG, HA, c-myc) or with an antibody to the native protein.
The cross-linking of POI-DNA complexes is reversed (usually by heating) and the DNA strands are purified. For the rest of the workflow, the POI is no longer necessary.
After an amplification and denaturation step, the single-stranded DNA fragments are labeled with a fluorescent tag such as Cy5 or Alexa 647.
Finally, the fragments are poured over the surface of the DNA microarray, which is spotted with short, single-stranded sequences that cover the genomic portion of interest. Whenever a labeled fragment "finds" a complementary fragment on the array, they will hybridize and form again a double-stranded DNA fragment.