DNA polymerase is responsible for covalently linking the deoxyribonucleotide monophosphate to the 3' end of the growing strand. Different organisms have different kinds of DNA polymerases, each with different functions such as proof-reading, polymerization and removal of RNA primers once they're no longer needed.
Once helicase has unwound the double helix and split DNA, replication can begin.
Each of the two strands acts as a template for the formation of a new strand. Assembly of these new strands is carried out by the enzyme DNA polymerase.
DNA polymerase always moves along the template strand in the same direction, adding one nucleotide at a time.
Free nucleotide with each of the four possible bases are available in the area where DNA is being replicated. . DNA polymerase brings nucleotides into the position where hydrogen bond could form, but unless this happens and a complementary base pair is formed the nucleotide breaks away.
Once a nucleotide with the correct base has been brought into position and hydrogen bonds have been formed between the two bases, DNA polymerase links it to the end of the new strand by making a covalent bond between the phosphate group of the free nucleotide and the sugar of the nucleotide at the existing end of the other strand. The pentose sugar is 3' terminal and phosphate 5' terminal, so DNA polymerase adds on the 5' terminal of he free nucleotide to the 3' terminal of the existing strand.
DNA polymerase gradually moves along the template strand, assembling the new strand with a base sequence complementary to the template strand. It does this with a high degree of fidelity (low mistakes).