Explain in detail (i.e., at the level of chemical structures and atoms) the reaction between ...

DNA is a polymer of nucleotides ( nitrogenous base + deoxyribose + phosphate group ). Within DNA nucleotides occur as nucleoside monophosphates ( a nucleoside is the nitrogenous base + deoxyribose ). However the nucleotides that serve for polymerization are nucleoside triphoshpates. Two adjacent nucleotides are always joined by phosphodiester bond. During formation of phosphodiester bond between two nucleotides, the added nucleotide loses two of the three phosphates in order to supply the required energy. A phosphodiester bond is always made between phosphates ( carried by 5-carbon of deoxyribose) of the incoming nucleotide and OH group ( held by 3-carbon of deoxyribose ) of the growing polymer. Therefore, a chain of nucleotides is lengthened in the 5-3 direction.

I don't know how to attach photos, so if you have them or if anyone else can post pictures of nucleotides with the carbons numbered and the different types of bonds labeled on the figure it would make the above paragraph much clearer.

Thanks Karim, animations are always easier to visualize than pictures... Check this out.

http://highered.mcgraw-hill.com/olcweb/cgi/pluginpop.cgi?it=swf::535::535::/sites/dl/free/0072437316/120076/bio23.swf::How%20Nucleotides%20are%20Added%20in%20DNA%20Replication