Speciation (the formation of a new species) can be broken down into a few concise steps.
The most important step is the isolation of two populations. This usually occurs because of physical factors such as a lake drying up and being separated into two smaller lakes.
As a result the fish in each lake are no longer able to breed with the fish in the other lake, resulting in no alleles being transferred between the populations.
Within each population mutations (random changes in the base sequence of DNA) will occur. But importantly since the changes are random the mutations that occur in each population will be different.
Similarly since both populations are now in different environments, physical characteristics of each enviroment such as water temperature will vary. As a result a mutation which may be favourable to cooler water conditions such as a thicker fat layer, may be favourable to one population of fish but detrimental to the other where the water is warmer.
As a result of differing selection pressures due to the differences in physical conditions(example above), both populations will evolve in separate directions to favour their new environment. This will lead to greater and greater genetic differences between the populations over time as a result of changing allele frequencies.
Eventually both populations even if no longer physically isolated will be reproductively isolated. Reproductive isolation is where both populations are no longer able to interbreed to produce fertile offspring, a requirement for an individual species.
Reproductive isolation can occur due to factors such as incompatible genitalia and non overlapping mating seasons. But importantly when two populations can no longer reproduce to produce fertile offspring they are considered two separate species.