To be fair, most people are willing to accept the process of natural selection - that is, the notion that the creature that can best adapt will survive and those that cannot will die. T This is actually a readily tested theory as one can point to the extinction of any creature in modern day and as an example of failure to adapt, or point to notable cases (such as the moths in england during the Industrial Revolution) as an example where adaptation worked just fine. The theoritical part is the assumption that there is a capcity for spontaneous genetic mutation, which has more than a little credability. Bacteria for example is proven itself fully capable of such things, and even complex organisms demonstrate this (cancer for example is the result of genetic mutation).
The theory of evolution is simply a statement that, over a long enough period of time, the minor changes forced by natural selection would produce an overall change in a species. This may be something as simple as the relative rarity of an albino squirrel (they find it difficult to hide from predators and thus don't often live long enough to reproduce). Evolution is little more than a logical extension of the idea of natural selection. This one is a little more difficult to test unfortunately as it takes many generations to produce a change in the population.
Speciation is the result of carrying the logic of natural selection to it's conclusion. Simply put, if changes in an environment will favor one genetic mutation over another over time this will result in a shift in the population to favor this successful mutation. Over a long enough period of time, such minor shifts would resonably result in a creature that can be classified as different from a starting point. If you carry this out over an extremely long period (say 50,000 generations or so), it would be reasonable to assume that there may only be a rudimentary similarity to the starting species.
Of the three, speciation is the hardest to prove because it relies on such a long period of time that direct testing is nearly impossible. The only recourse is to rely on the fossil record in an attempt to determine if there is a pattern that can be followed. This procedure is obviously going to generate a lot of flack becasue one cannot actually directly observe the process and must instead induce what may have happened. What's worse, is many people tend to believe (fundamentalists primarily) that the very idea of speciation is blasphemy. Others simply find it distasteful to believe that their most distant ancestor might have simply been a particularly complex chemical in a tidewater pool.
To those that believe evolution and the like blasphemy, I would submit that there is no reason such an explantion cannot coexist with the teachings of your religion. While evolution might not be as incredible as simply snaping one's fingers and creating all the life on earth, who's to say what process an intelligent designer might leverage to get his intended result. And for those who find the notion of evolution distasteful because of what it implies, remember - you're almost certainly only a handful of generations removed from people who used their hands for toilet paper and married their cousins. Besides, at the core of it all, life is nothing more than a fantastically complex series of chemical reactions and interactions