Well, the Alternating Phosphate and deoxyribose sugars make up the sides of the DNA. Hydrogen bonds hold the Nitrogen bases (Adenine, Cytosine, Guanine, and Thymine) together. So the simple answer would be 'hydrogen bonds hold nitrogenous bases together. Adenine and Thymine, when met, form two hydrogen bonds, while Cytosine and Guanine form three hydrogen bonds, thus holding them together! :) I know it's a lengthy answer, but it's quite simple once you get the basics down. :)
