Most DNA dyes are intercalators. They slip in between the bases and become more fluorescent as a result. Some dyes, such as Hoechst 33258 and 33342, bind along the major or minor grooves of the DNA and become more fluorescent when they bind.
your question is too vague and you must define at first the kinds of DNA and the kind of dyes.
Do you want to work in vivo or in vitro?
DNA as macromolecule has been extensively studied over more decades and if you give your question (copy, insert in google or google scholar) you ´ll earn a plenty of hits.
What is the reaction occur between dyes and DNA through staining?
9.130.000 hits for google!!!!
My comments:
-At first search papers and books about the structure of various DNAs.
Most DNA dyes are intercalators. They slip in between the bases and become more fluorescent as a result. Some dyes, such as Hoechst 33258 and 33342, bind along the major or minor grooves of the DNA and become more fluorescent when they bind.