the replicative DNA polymerase
/ po-LIM-er-ase /
If the replisome is the factory, DNA polymerase is the worker on the line who actually adds the new building blocks one by one. It is the central enzyme of replication: it reads a single DNA strand and builds the complementary new strand, nucleotide by nucleotide, getting the sequence right.
DNA polymerase works under two strict rules that shape everything about replication. First, it can only add new nucleotides to the 3' end of a growing strand, so the new strand always grows in the 5'-to-3' direction (and the template is read 3'-to-5'). Second, it cannot start a strand from scratch — it must extend an existing primer's free 3' end. For each step, it selects the nucleotide whose base correctly pairs with the template (A across from T, G across from C), forms a phosphodiester bond to add it, and moves on. Many replicative polymerases also carry a built-in proofreading 3'-to-5' exonuclease that backs up and removes a wrong base before continuing, giving very high accuracy.
Different organisms use different replicative polymerases — DNA polymerase III in bacteria like E. coli; polymerases delta and epsilon in eukaryotes — but the chemistry and rules are the same. The two rules together (5'-to-3' only, primer required) are exactly why one strand is copied smoothly (leading) while the other has to be built in pieces (lagging). Cells also have other polymerases for repair and for getting past damage, but the replicative polymerase is the fast, accurate one built for copying the whole genome.
Reading a template 3'-T A C G G-5', the polymerase adds 5'-A T G C C-3' to the primer's 3' end, picking each base by Watson-Crick pairing. If it accidentally inserts a G opposite an A, its proofreading exonuclease snips the wrong base off before adding the next one.
Extends only 5'-to-3', only onto a primer, base by base.
Saying the new strand is read 3'-to-5' is wrong — the template is read 3'-to-5', but the new strand is synthesized 5'-to-3'. Keep clear which strand the direction refers to.