Take a human physical trait like handedness. Your dominant hand is determined, in a simplified model, by the presence of a certain gene at a certain position on your chromosomes. A biologist will look at the entire human genetic pool, the collection of each person's genetic makeup, and determine that 11 percent of handedness genes are of the L-type right now. Jump ahead 50 years, and a biologist might survey the pool again, discovering that the percentage of L-genes has fallen to 9 percent. And that's it.
Evolution looks uncontroversial.
The exciting part is in trying to figure out the mechanisms that bring about these changes in the genetic pool, not the evolution itself. The three most important mechanisms for bringing about evolutionary change are natural selection, genetic drift and mutation. Within a species, some particular trait will afford a slight advantage to those individuals who possess it. This will lead to increased reproduction on the part of the advantaged individuals and, hence, the passing on of the genetic trait to its more abundant offspring. Over many generations, this imbalance, no matter how slight, leads to the trait becoming widespread throughout the species.