DNA replication:

Helicase is an enzyme that unwinds DNA
The point where the splitting begins is called the replication fork, it has a top strand(leading strand) and a bottom strand(lagging strand)
The unwound sections are used as templates to create complimentary DNA strands
RNA primase places a section of RNA called a primer, this primer tells the DNA polymerase(enzyme) where to start adding matching nucleotides
DNA polymerase can only copy strands in the 5' 3' direction
(moves from 3' to 5' direction relative to the template strand)

For the leading strand, the primer is only placed once since the polymerase moves in the same direction as the helicase
In the lagging strand, the primer needs to be placed multiple times
This is because the polymerase reaches the end without replicating the part that got unzipped by the helicase after it started.
The fragments formed due to this are called okazaki fragments.
A different type of DNA polymerase the goes and replaces the primers with DNA
The fragments are then joined together by an enzyme called DNA ligase

The entire process is really accurate (1 in 10 billion nucleotides are wrong)

DNA polymerase is mainly 3 enzymes.
DNA polymerase 1 (Removes primer,DNA repair), DNA polymerase 2 (DNA repair) and DNA polymerase 3 (placing the corresponding nucleotide)