The three basic requirements for evolution
through natural selection (as told by the anthropology
textbook used in ANTH 1001 at the University of Minnesota
Genetic variation in a species
Heritability of the variation
Differential reproductive success
This is essentially the same as what melodrame stated, but simpler.
Contrary to popular belief, natural selection does not necessarily imply increased survivability of a species, but only a change in survivability. It works both ways, wherein a trait can be selected for or against (or have no change in the survivability of the species).
There are three basic types of natural selection as well:
1. Directional Selection: Selecting for taller people, resulting in overall higher mean heights of a population.
2. Disruptive Selection: Selecting for either the tallest or the shortest, resulting in a similar average height, but two populations with much higher or much lower local averages.
3. Stabilizing Selection: Opposite of Disruptive selection; selection against the tallest/shortest of a population, reducing variation of that trait.