For example, arthropods all have chitinous exoskeleton, hemocoel, and jointed legs. Insects have all these plus head-thorax-abdomen body plan and 6 legs. Flies have all that plus two wings and halteres. Calypterate flies have all that plus a certain style of antennae, wing veins, and sutures on the face and back. You will never find the distinguishing features of calypterate flies on a non-fly, much less on a non-insect or non-arthropod.

Dogs are another example. There should be species we would group with dogs, and there are - such as wolves and coyotes. So we are not surprised when dogs and foxes turn out to share some peculiar features of the middle ear. This group - the Family Canidae - can be grouped with the bears, raccoons and weasels, because their ears have some similarities to those of dogs. All of these have carnassial teeth, but so do cats, civets and seals - so we group the entire lot as being Order Carnivora. Carnivores all have 3 middle ear bones, mammary glands, placental development, hair, a diaphragm, a four-chambered heart, and a larynx. But they share those features with humans, bats, elephants and whales. So we group that entire lot as being Class Mammalia. But mammals have amniote eggs, and so do birds, lizards, snakes and turtles. And amniote animals share with frogs and salamanders the property of having four legs - they're tetrapods. Tetrapods and fish both have backbones - they're vertebrates. Vertebrates and starfish are both deuterostomes because they share the way their embryos develop a mouth. Deuterostomes are left-right symmetric, so we group them and insects and snails as bilateral. The bilaterals, the jellyfish and sponges are all animals. Animals, fungi, rose bushes and amoebas all have a nucleus inside each cell - they're eukaryotes. Eukaryotes and bacteria and archaea share the DNA mechanism, lipid-based cell membranes, and hundreds of other biochemical details.

(And that's the short version of the story! For all the fancy Latin names, see the Tree of Life.)

Notice that the dog-to-bacteria story has some apparent irregularities. For example, I said that elephants and whales are mammals, and that mammals have hair. It is not obvious, but elephants and whales do have a small amount of hair. Also, scientists group whales and snakes as tetrapods. So where are their four legs? From the theory of Common Descent, we see that they must be descended from four-legged creatures, and that they have lost their legs. (Loss is an easy mutation - as witness hairless dogs.) So, we predict that there should be fossils of whales with legs, and snakes with legs. These fossils have been found. Similarly, starfish outwardly have radial symmetry, but we classified them as bilateral. So Common Descent predicts that their group (echinoderms) had bilateral ancestors, and such a fossil has been found.