In eukaryotic cells, DNA replication occurs in the nucleus during the S phase of the cell cycle. The cell's total DNA is found in the nucleus, which is why replication occurs there.
DNA replication occurs in many steps. First, the double-stranded DNA must be unzipped and separated. Once separated, the unpaired nucleotides on each strand act as a template for new nucleotides to arrive and pair up. New strands of nucleotides are assembled, and they become covalently bonded to the two separate, single strands of DNA. The nucleotides assemble in a complementary order and fuse with the single-stranded DNA to form two new daughter strands of DNA that can exit the cell.