We investigate the DNA-silica binding mechanism using molecular dynamics simulations. This system is of technological importance, and also of interest to explore how negatively charged DNA can bind to a silica surface, which is also negatively charged at pH values above its isoelectric point near pH 3. We find that the two major binding mechanisms are attractive interactions between DNA phosphate and surface silanol groups and hydrophobic bonding between DNA base and silica hydrophobic region. Umbrella sampling and the weighted histogram analysis method (WHAM) are used to calculate the free energy surface for detachment of DNA from a binding configuration to a location far from the silica surface. Several factors explain why single-stranded DNA (ssDNA) has been observed to be more strongly attracted to silica than double-stranded (dsDNA): (1) ssDNA is more flexible and therefore able to maximize the number of binding interactions. (2) ssDNA has free unpaired bases to form hydrophobic attachment to silica while dsDNA has to break hydrogen bonds with base partners to get free bases. (3) The linear charge density of dsDNA is twice that of ssDNA. We devise a procedure to approximate the atomic forces between biomolecules and amorphous silica to enable large-scale biomolecule-silica simulations as reported here.