Humans are born with mutations every day. As in other species, most of the mutations do not increase the chances of reproductive success. Look at the statistics for the number of children who are born with heart defects, cleft palates, extra fingers/toes, missing fingers/toes, spina bifida, and the list goes on.
As far as the rate of evolutionary change... There are almost 7 billion humans alive right now. Suppose one man was born normal in every way but with one new ability that was very attractive, say, he could fly. He would reach reproductive maturity in ~ 15 years. Then the question is how many women could he get pregnant and how many of his children would be born with the same ability? Lets say he was really busy and had sex with a different women every day and they all got pregnant and 100% of his children could fly and he lived to be 85 years old. In 70 years, he would father 25,550 children. Compared to 7 billion (or maybe 8 billion by the time he dies), this is not enough to change the evolution of the human species.
On the other hand, if a space alien microbe landed on earth today, started reproducing wildly and it killed every human being who did not have red hair, within a year, the only humans left to reproduce would be those with red hair. In this case, in a couple of generations, the human population would evolve to have red hair. Of course there would not be 7 billion humans anymore.
If you are really interested, study evolutionary biology.