Take the time to watch the Crash Course video, Population Genetics: When Darwin Met Mendel. The key concepts you need to pay attention to in this video are: gene flow, genetic drift, bottleneck effect, sexual selection and founder effect.
To sum up some of the key points:
Gene flow - occurs when individuals join new populations and reproduce, this is what keeps neighboring populations similar. Low gene flow increases the chance that two populations will eventually evolve into different species
Genetic drift - is a change in allele frequency due to chance, this causes a loss of genetic diversity. This is common in small populations, and it can be caused by a population bottleneck. Genetic drift can have negative effects on a population
Founder effect - this occurs after the start of a new population
Sexual selection occurs when certain traits increase mating success
For a short review, visit these Berkeley Evolution 101 pages: