Evolutionary change is not a single mechanism. Mutations introduce genetic variation. Natural selection can increase variants that improve reproductive success in a particular environment. Genetic drift can change the frequency of variants without selection, especially in small populations. Recombination produces new combinations of existing variants.
Other processes can produce larger genetic changes. Genes can be duplicated, deleted, rearranged, or placed under different regulatory control. Existing proteins can acquire altered activities, and populations can diverge until reproductive isolation develops.
These processes can be observed through genetics, laboratory experiments, comparative genomics, and studies of natural populations.
Experimental evolution has documented adaptation over many generations. The Lenski long-term E. coli experiment provides a particularly detailed example in which a population acquired aerobic citrate utilization and researchers subsequently identified genetic changes associated with the new phenotype.
Studies of gene duplication, protein evolution, regulatory change, and speciation provide additional evidence that evolutionary mechanisms can produce meaningful genetic and phenotypic change.
Demonstrating that a mechanism can produce change does not by itself establish that the same mechanism produced every biological structure found in the history of life. Different evolutionary questions involve different scales, genetic systems, populations, and periods of time.
How far can experimentally demonstrated evolutionary processes be extrapolated when reconstructing ancient biological innovations? Which historical transitions can be connected to specific genetic and developmental pathways?
Intelligent Design need not depend upon denying mutation, natural selection, gene duplication, speciation, or other demonstrated evolutionary processes. The design question concerns their explanatory reach: what these processes have been shown to produce and whether they adequately account for particular complex biological innovations.