DNA-carbon nanotube hybrids (DNA-NT) are novel nanoscale materials that consist of single walled carbon nanotubes (SWNT) coated with a self-assembled monolayer of single stranded DNA (ssDNA). Many recent experiments involving DNA-NT have shown that this material holds a wide range of technologically useful properties such as facilitation of SWNT sorting, chemical sensing and detection of DNA hybridization. Despite the importance of DNA-NT, a detailed understanding of its microscopic structure and interactions are lacking. To address these issues we have performed classical all-atom molecular dynamics (MD) simulations using empirical force fields. MD reveals the nature of the interactions and structural arrangements involved in DNA-NT. We find that the hybrid material spontaneously self-assembles via the attractive pi-pi stacking interaction between ssDNA nucleobases and SWNT outer wall. Under ambient conditions, ssDNA can adopt various wrapping conformations about SWNT including right- and left-handed helices as well as disordered, kinked structures. Helical wrapping is driven by asymmetric torsional forces in the sugar-phosphate backbone that result in ssDNA wrapping from the 3' end to the 5' end.