The enzyme DNA helicase breaks the hydrogen bonds between the two polynucloetide DNA strands causing the double helix to unzip, forming two single strands.
Each original single strand then acts as a template for a new strand. Free-floating DNA nucloetides join to the exposed bases on each original template strand via complementary base pairing.
The nucloetides of the new strands are joined together by the enzyme DNA polymerase. This forms the sugar-phosphate backbone. Hydrogen bonds form between the bases on the original and new strand and the strands twist to reform the double helix.
Each new DNA molecule contains one strand from the original DNA molecule and one new strand, hence the term semi-conservative replication.