The enzyme that joins the nucleotides of a DNA strand together is called DNA polymerase.

Here's how it works:

* DNA polymerase reads the existing DNA strand as a template and adds the complementary nucleotides one by one.

* It forms a phosphodiester bond between the phosphate group of the new nucleotide and the sugar of the previous one. This creates the sugar-phosphate backbone of the new DNA strand.

There are several types of DNA polymerases, each with different roles in DNA replication and repair.