The process is rather like compound interest. As an example, take a population of 1000 organisms; on average each organism has one descendant in the next generation. Now let a beneficial mutation appear with a 1% advantage, so the mutated organism will have on average 1.01 descendants in the next generation. For comparison I include ten other mutated organisms with a deleterious mutation, giving a 1% disadvantage. Start with a population of 10 deleterious, 989 neutral (or unmutated) and 1 beneficial mutations. See what happens if we let the population reproduce for one thousand generations: