In the United States, we put marks on our coins to show where they were produced. If the letter 'D' is on the bottom right side of the heads side then it was made in Denver, Colorado. Likewise, 'P' stands for Philadelphia (sometimes no mint mark), 'S' for San Francisco, 'W' for West Point, etc.
Similarly to how we can look at this coin and know where it came from we can look at species today and find signs of the past generations which they came from.
Claim: Descent with modification--species have changed over generations.
Predictions: We would find signs of past generations, remnants of where species came from. These remnants might come in the form of repurposed traits, maladative traits, non-adaptive traits, or the lack of sensible traits.
Falsification: Species are completely unique and unlike other species. They are perfectly adapted to their environment.
Observations: Vestigial Structures, pseudogenes, atavistisms (see examples below).
Corroboration: The vestigial structure is found to be homologous to another species structure. The trait is found to be injurious or does not give an adaptive advantage.
Inference: Species only have what mutation and past generations gave them. Repurposed, maladaptive traits, nonadaptive traits, and missing reasonable traits are all signs of species natural origin.
If evolution is true, we should be able to find leftovers from past generations with species--anatomy or genes that tell of where they came from. How would we show that they are vestigial as opposed to adaptations? Well, we'd need to show that they have little or no connection to their original adaptive purpose or in some cases even hurt the species' survival and reproduction capabilities. Also important here is how homologous they are to other species. While often exhibiting awe-inspiring adaptations, species are flawed and imperfect. Species only have what past generations gave them.
Locomotion transitions: Some of the best examples of vestigial structures come from species that have made a transition from locomotion on land, water, or air to a different medium (for instance whales from land to sea, birds from land to air, legless lizards from land to subteranean, etc.). Being conscious of this pattern can allow you to find your own examples of remnants! Please comment them at the bottom of this page!
Below is a fetal fin whale showing the vestigial tooth buds within their jaw.While whales don't typically have external legs (though whaling tales do exist) they do have the remnants of internal ones and the pelvises that supported them. The occurrence of these left over parts also extends to dolphins that very rarely will actually have external "legs." The limbs are also visible en utero. Hair is another sign of cetacean land origins. Manatee fingernails and hair Recurrent Laryngeal Nerve Amphiumas' vestigial legs Salamanders evolving towards leglessness Some snakes also have the remnants of legs and pelvises that are used by males to help grip females during mating. Legless lizards are another example of leftover limbs. A few other resources on leglessness: http://life.bio.sunysb.edu/ee/wienslab/wienspdfs/2009/Evolution_of_Limblessness.pdf http://whitelab.biology.dal.ca/lb/Bejder%20and%20Hall.pdf http://etb-visual-evolution.blogspot.com/2012/05/snakes-with-legs-snake-evolution.html http://www.flickr.com/photos/stephenmahony/8530271046/ http://www.flickriver.com/photos/tags/wormskink/interesting/ http://gretelinaustralia.wordpress.com/2012/03/07/reptilien/ Dinosaur Arms - a similar series of changes took place with certain dinosaurs that no longer had much need for arms or fingers. here for more illustrations on this. This change, however, is still in process and has left a number of remnants that teach us about the horse's ancestral past. Read more: http://ncse.com/rncse/30/4/vestigial-structures-exist-even-within-creationist-paradigm The horse vestigial bone structures don't end there. The ulna and fibula also show signs of being remnants of past forms. Blindness helps us see evolution A very long list of cave and subterranean species could be produced that demonstrate the reduction and mutation of eyes. For some species the eyes (but often not the sockets) are completely gone or so reduced that they are almost not visible. Subterranean or fossorial eyes similarly show us the vestigiality. (Numerous examples could be listed here. Pinniped Ears Pinniped nails Koala Skulls Stapedial Artery Blind Spot Genetic Remnants, aka Atavisms (see whales at top of page, as well) - Pseudogenes More on human pseudogenes: http://www.talkorigins.org/faqs/comdesc/section2.html#mol_vestiges http://en.wikipedia.org/wiki/Human_disabled_pseudogenes_list http://www.uam.es/personal_pdi/ciencias/genhum/bibliogenoma/pseudogenes2004.pdf http://www.ncbi.nlm.nih.gov/pmc/articles/PMC403797/ http://www.pseudogene.org/human/index.php