Basic natural selection:
1. One population of the same species is cut into 2 or more groups. Maybe by a landslide. Migration, anything.
2. The species cut off from the main population experiences environments they've never seen before.
3. Many of the separated species die. Leaving the strongest and the ones with the most favourable features, such as thick fur if if its cold, to live and reproduce. Passing on their genes to their offspring and eventually creates a new population with these features.
4. Eventually, the variation in the new population caused by mutations in genes, become so different to the main population. They cannot interbreed anymore and thus makes them a different species.