There are number of ways that speciation can occur:
1. Mainly geographical split which causes 2 populations to form in 2 different environents thus different selective pressures cause them to change over time. This is called allopatric speciation
2. The other main one is sympatric speciation, though rarer, can still occur. This is when NO geographical split occurs and a population changes due to selective breeding where one group may prefer different mates, thus slowly leading towards different reproduction time periods (example). WHen this occurs over time the population becomes split into two since there is no gene flow between them.
3. Changes in population size can also cause speciation where genetic drift, founder effect and bottleneck effect causes changes in allele frequencies and causes a "modification" of a species not necessary a population splitting into two species. For example, an introduction of a new predator to a group of deers may cause all of the deers to have longer legs. and over time become a completely new species.
The key thing to remember is... ALLELE FREQUENCIES and they are caused by MUTATIONS.