How does the mRNA molecule carry information to DNA?

The question is a little bit incorrect.  mRNA does not carry genetic information to DNA.  mRNA carries the genetic information from the DNA to a ribosome.  The ribosome will then "read" the mRNA strand and make a protein.  The entire process is called protein synthesis and can be divided into two main steps.  

Step one is called transcription.  Transcription is the copying down of the DNA message into RNA format.  A special enzyme called RNA polymerase will "unzip" the DNA molecule far enough to where corresponding RNA bases will match up with the DNA bases.  It works the same as DNA replication with one exception.  RNA does not have thymine.  It has uracil instead.  That means the base pairing is as follows A-U and C-G.  Eventually the RNA strand is complete.  It is called an mRNA strand because it will leave the nucleus and deliver its message to a waiting ribosome.  It acts as a messenger RNA.  

Step two is called translation.  Translation involves the ribosome translating the mRNA message and using it to make a chain of amino acids (a protein).  The mRNA is read three bases at a time.  That 3 base sequence is called a  codon.  Special tRNA (transfer) molecules will pair up with each codon and drop off an amino acid.  The tRNA molecules will continue to drop off amino acids in the correct order until the protein is complete.  The following video should help you visualize what is going on.