Perhaps the most common misunderstanding that prevents people from grasping evolution is complexity.
We see it almost daily on the forum where people mention DNA or the eye or any of a multititude of examples and ask how it could have arose "by blind chance"?
Whenever you see a reference to chance and complexity it is obvious the person hasn't yet grasped the basics of the theory. Chance is only one part of the process. The other important part, the one that Darwin discovered, is natural selection.
Natural selection is a "chance accumulator". Dawkins illustrated it in "The Blind Watchmaker" using the well-known creationist challenge of monkeys, typewriters and Shakespeare.
Take the line from Hamlet, "Methinks it is like a weasel".
The chances of monkeys with typewriters producing this phrase exactly is 1 in 10,000 million million million million million million.
This is what we might call single-step selection
However if we apply a cumulative-selection process it becomes very easy to produce this phrase.
First the computer produces a random line of 28 characters.
Next it "breeds" from this first generation by producing multiple copies of it but with a certain amount of random error or mutation built in.
Now the computer selects the second generation that is closest to target phrase.
and so on...
The programme wasn't trying to create the target phrase it was simply producing random mutations and then selecting the one that looked the most promising.
It turned out the phrase "Methinks it is like a weasel" in just 48 generations.
It illustrates quite well how evolution by natural selection works.
Genes suffer mutations which cause unpredictable changes in the bodies they build. If the change is even very, very slightly beneficial, that body has a better chance of passing on that gene to the next generation until it becomes ubiquitous in the gene pool. Complexity accumulates through lots of very small steps.
When people express incredulity about natural processes producing complexity it is usually because they are thinking in terms of single-step selection.
Hopefully this helps and might whet somebodies appetite to investigate furhter. "The Blind Watchmaker" is an excellent resource to challenge most of the creationist objections we were taught in Watchtower publications.