I find that when most people say they do not believe in evolution, they often demonstrate a poor understanding of the mecanics of it at best. So I'm just going to try to post a simplified version of evolution.
Evolution occurs when a population of a species develops a trait/traits that separate it from it's parent species. Evolution is an ongoing process, not just a *insert animal here* turns into an *insert animal here*.
The basic mechanics of it are that a parent has offspring by some form of eproduction, and one of it's offspring has a genetic mutation that is beneficial (genetic mutations can be beneficial, harmfull or, usually, are not even noticable and make no difference to the survival of the individual), and helps that individual to survive (or in some cases help the group to survive) and make more babies. The more offspring an organism has, the more likely it is that the gene that was beneficial is passed on to more and more individuals in a population.
Lets say there is a species of, say, Ramlehorns. The original population of ramblehorns has 3 horns. Some of the population finds itself in a new environment that is much drier than it's original environment. Since horns take up a lot of resourses to grow, the animals are worse off because of the decrease in vegitation in their new environment, where before three horns were a boon in that they attracted mates. However, one individual has a genetic mutation that causes it to have no horns. The resources (food, water) that would've gone to the horns are now free to help the individual survive and, wait for it, make more bebehs. These offspring also have the mutation, and are also more sucsessful at producing offspring. Eventually, the whole population has no horns. After thousands of years, and other genetic mutations that helped reproduction/survival like shorter coats, larger ears, better water retention, the split off population of ramblehorns is no longer able to reproduce with it's parent species. It is now it's own species, lets call them ramblers. There you have it, evolution.
With millions of years of constant evironmental pressures the variaty we see in todays biodiversity is hardly supprising.
Just to clear up a few misconceptions about evolution:
Evolution =/= abiogenisis.
Evolution =/= the big bang. Evolution is a biological process that is well observed, understood, and as close to proved as can be in science. Asking evolution to answer to the big bang is like asking gravity to explain where matter came from.
Theory in science does NOT mean the same thing a theory in everyday speech. To become a theory needs loads of evidence, and is as close to proven as can get. A theory, as people normally use the term, is more like a hypothesis in science.
Darwin never renounced his theory, and the theory of evolution did not end with Darwin, research still continues. (Scientific theories like evolution or gravity, which is also a theory, are under constant scrutinization by many people.)
Many theists can and do believe in evolution.
Not all atheists believe in evolution.
There, I hope that helps out. If anyone has any further questions about evolution, or if I missed anything in there, just ask. My internet turns off in a few minuites, but I'll be back tomorrow.