Reporter enzymes typically include alkaline phosphatase or luciferase. In the presence of the appropriate substrate, alkaline phosphatase leaves a purple precipitate. So, your test protein becomes 'visible' as a purple band. For luciferase, in the presence of the appropriate substrate, light is emitted, which can be captured on film. When a protein binds to DNA, it decreases the net charge of the protein and gives the complex more frictional drag.
Complexes are 'visualized' as bands using autoradiography.
The DNA is usually radiolabelled. In a population of identical fragments, an average of one nick per DNA molecule is made. One end of the DNA is usually radiolabelled. A ladder of bands is observed. If a protein is bound to a particular DNA sequence, it will block DNase I from nicking the DNA at that site.