DNA replication is semi-conservative, meaning existing strands are used as templates for new strands. The DNA is separated (unwinds) by the enzyme helicase. This enzyme breaks the H bonds between nucleotides. Topoisomerase breaks the DNA ahead of the opening of the replication fork before it gets to tight (to reduce tension). An enzyme called primase starts a short RNA chain from scratch using RNA nucleotides. Now DNA polymerase can build the new DNA strand using complementary base pairing (Adenine - Guanine, Cytosine - Uracil) in the 5' to 3' direction.
The second strand is built up by joining segments called Okazaki fragments using the enzyme DNA ligase. This occurs in the 3' to 5' direction and makes phosphodiester bonds.
This results in the formation of 2 identical DNA complexes.