I am not an expert on evolution but I will give it a shot at explaining it briefly with what I have gleaned about evolution so far from people, who are actually interested in understanding evolution, get their knowledge from scientists or are scientists.
Evolution: is a process that takes millions, even billions, of years and is difficult to observe over a short timescale. Basically, there are billions of different organisms on earth of varying similarity, and we label them in our own human way. This means that when people argue against evolution from one species to another they are making all sorts of errors. Evolution is more complex than most people realise, and many fail to properly appreciate the various mechanisms involved. Those factors are: Adaptation, Genetic drift, Gene flow, Mutation, Natural selection, Speciation.
The human common decent fossil evidence shows a gradual move from the chimpanzee-like Australopithecus, through Homo Habilis, Homo Erectus (and various others) to Homo Sapiens, over millions of years. There are millions of other fossils, there are archaeological findings that reveal the migration of man out of Africa, there is the cross-breeding of animals and plants that we do to day, and there is DNA, amongst many other things. Evolution is simple common sense. We share over 98% of our DNA with chimpanzees. Why? Only primates need to take in vitamin C with their food as there bodies cannot make vitamin C. This proves a shared ancestor. We are genetically closer to chimpanzees than mice are to rats. Life is more connected than anything bible writers knew about. DNA proves this and we use DNA in paternity testing, breeding of dogs, to solve crimes, to understand disease, etc. Humans not only share a common ancestor with apes (and, technically, are apes), but we share a common ancestor with our pets, and our food, and the trees, plants etc . We have coded the genome, we have mapped out the tree of life, we have lots of fossils, and we utilise artificial natural selection by; breeding cows, tomatoes, crops to be larger, stronger and higher yielding etc. I challenge any evolution denier, when offered gene therapy to proactively cure a terminal disease they will get later in their life, to turn down the therapy on account of genes and evolution being against what the Bible says.
Remember that nature is competitive. It's a struggle to survive, so any advantage an organism can get is likely to be passed on. To use a recent example, there are now bacteria that can digest nylon. This is significant because nylon is a recent human invention. So the bacteria in question are exploiting a resource that helps it survive. Not all bacteria do this, as they're adapted to their own ecological niches. But nylon-eating bacteria exist for the same reason; they're exploiting a new niche thanks to a mutation that exploits a food resource which in turn allows for more of those organisms to propagate. It took a mutation in bacteria to begin to utilise this material as a food source. No one ever suspected that chemical polymers could provide ecological niches capable of exploitation by mutant bacteria, but the evidence shows not only that it is possible but that it is a fact. The reason that bacteria show us so much about evolution is because their reproductive rate is so much faster than ours. In the last 2,000 years, humans have gone through approximately 100 generations. Bacteria accomplish that in hours.
Motor cars have evolved from what worked before just like the human genome evolved. The first cars were not today's cars even though all the main parts that make up today's cars existed a hundred years ago. Nobody set car design in motion with the idea of today's cars, roads, highways, toll roads etc. These just happened or evolved as the requirements changed. There is no single designer of your car today. Cars of the future will evolve from today's designs and so will the technology. Products once used by your parents; videos, Sony Walkman, Kodak film, LP records, tapes, etc have become obsolete. So long as humans find use in the design, they'll pass them on and modify them. Nature is doing the same over time with our genomes. However nature is rather slow, cruel, and wasteful and it is obvious there is no intelligent designer behind it.
Our scientific knowledge evolves as well. We know things today that we did not even know twenty years ago. (Hubble telescope, Human Genome Mapping, etc)
