How is genetic information stored in the base sequences in DNA?

DNA has four nitrogen bases.  They are abbreviated A, T, C, and G.  A and T can pair up, and C and G pair up.  This is why they are referred to as base pairs.  Human DNA has approximately 3 billion base pairs.  Regardless of the species, though, it is the order of the base pairs that matters.  A strand of DNA contains the stored information that determines how to make proteins.  A sequence of DNA will get "read" and "transcribed" into a strand of RNA.  RNA does not have the "T" nitrogen base.  Instead it uses uracil, which is abbreviated "U."  The RNA strand will then get translated at a ribosome.  Think of the ribosome like a protein factory.  The RNA tells the ribosome which piece goes where and when it goes there.  The "pieces" are amino acids, and a string of amino acids is a protein.  Those proteins eventually determine an organism's phenotype as determined by thousands of traits. 
When the RNA strand makes it to the ribosome, the ribosome will read the base pairs in groups of three.  This is called a codon.  Let us use a random sequence of 9 bases.  AUCGGCAGU.  That strand of 9 bases contains 3 codons.  AUC-GGC-AGU.  Each codon corresponds to a specific amino acid.  AUC = isoleucine.  GGC = glycine.  AGU = serine.  In reality, the amino acid chain will be hundreds of pieces long.  Once the chain is complete, the protein is finished.  If the order of the bases was different, the corresponding codons would be different.  That would then change which amino acids get placed into the chain, producing an entirely different protein.  
https://learn.genetics.utah.edu/content/basics/transcribe/