In a nutshell, evolution is caused by a malfunction in the DNA processes due to its error-prone replication system which causes small or large mutations in the new copies of itself. These mutated copies are then thrown at Natural Selection where it tries to exterminate them into oblivion through a wide variety of tools such as miscarriage, starvation, disease or sexual avoidance.
Successful evolution occurs when a species generates an accidental mutation that just so happens to evade the Natural Selection Blender of Death. It doesn't have to be the fittest. It just has to have the right mutation at the right moment.
Most of these evolutionary mutations come about when a species is being pulverized by something - be it the weather or a new invasive predator. The smaller populations make inbreeding corruption rates significantly higher which makes mutation rates skyrocket. This high rate of mutation causes better chances for evolutionary adaptation at the expense of death, debilitation and disease which Natural Selection happily destroys into oblivion. These failed lines of genetic experimentation are what we see on the charts as extinction. The lines that continue are what we see as transitionals - random genetic accidents that shuffled the right amount of DNA into the right places.
Our own human lineage evolved from such an accident - the accidental fusion of chromosomes 12 and 13 in the offspring of an ancient primate that is now extinct.
And theres also a flip side to erroneous fusions. Human males are being born with an extra Y chromosome - called XYY syndrome. Its not fatal and causes no diseases. It only causes increased growth velocity in boys and an enhanced stature. It is living proof that added complexity can arise from random errors in DNA transcriptions. XYY males have an extra 50 million base pairs in their DNA compared to the rest of us which makes them a potentially new macroevolutionary genesis for humans - provided our population dwindles down to a few thousand people.
Among the many misconceptions, Evolution does not mean "development" or "improvement". Evolution is only about "change". Whether it is change for better or change for worse, it doesnt matter because Evolution is random. Sometimes a species evolves a certain trait that later causes its extinction like the desert chamelion that evolved a bright red spot which attracted more sexual partners thus overtaking the population - an evolutionary success. However, it later attracted the eyes of something else - the desert falcon - and now they are all extinct.
Evolution became a discovered fact of nature when we uncovered DNA's error-prone replication system and continues to yield expected results such as this: http://www.wired.com/wiredscience/2012/01/evolution-of-multicellularity/