So I'm going to run through a few basic things which lend heavy credence to the theory of evolution, since people are asking stupid questions, I'll sit on them at the end. So here's a neat experiment which I think came up earlier but may have been overlooked:
http://en.wikipedia.org/wiki/E._coli_long-term_evolution_experiment
Lenski's experiment is famous and one of my personal favourite experiments of all time. Extremely simple but extremely clever. It shows irrefutably that adaptations are swift and more importantly that over time changes can occur in a population which lead to vastly differing organisms.
Proof that it can happen is not proof that it did happen. Enter the fossil record. Now we are extraordinarily lucky to have any fossils and considering their rarity the abundance is a veritable blessing.
http://en.wikipedia.org/wiki/List_of_transitional_fossils
There are a few 'transitional' fossils. Bear in mind transitional means little in evolution because it is slow gradient which I'll come to in a second. Basically fossils show (and these are just organised to easily show this) that over time things have changed.
Slow gradient, it means that the changes are exceedingly slow, cripplingly so? Well, only in those that die out! Mutation (coincidentally frequency of mutation is why sexual reproduction is beneficial. Mutants are we get to enjoy sex) leads to changes but they are almost always tiny, miniscule changes. The examples for this are getting ridiculous but suffice to say any textbook or even straight book on the subject will provide a plethora of examples where minute changes lead to something impressive. The eye is always a favourite, unsurprisingly and many examples exist for it's progress.
Further evidence for evolution is the mistakes we have, my personal favourite is the recurrent laryngeal nerve:
http://www.youtube.com/watch?v=0cH2bkZfHw4
It is ridiculous isn't it?
Other evidence is the eye (surprisingly, think about how it's laid out, really think about it, something is the wrong way around...). The human appendix (uses: randomly kills you) is a vestigial organ like the coccyx is a vestigial tail slowly going away.
Now, that's a bit to chew through but trust me it doesn't even begin to scrape the surface of evidence, it really is tremendous, there is so much evidence out there for evolution it will take you years to view it all in it's entirety. That's why books summarise it.
Still, here are some of the more popular counter arguments and why they fail:
"Monkeys still exist, so why do humans exist as well?!"
Addressed in my other post, apes are a branch of the same ancestors as us, they are not our ancestors themselves. More importantly we aren't actually in direct competition.
"There are gaps in the fossil record!"
Yes, expectedly so. The fossil record is vast and almost comprehensive, the few remaining gaps are more than adequately explained. More importantly a gap doesn't mean anything, it's a lack of specific evidence rather than evidence against the theory itself.
"The Bible says X"
Well, the Koran says Y and on this bit of paper I've written Z. Religion is not the arbiter of truth or more precisely a book is not. It's a book (or collection of for the Bible), written by men thousands of years ago. It contains factual, historical and prophetical inaccuracies, it is not correct simply by virtue of it being correct, we don't do circular reasoning.
"Some scientists don't believe it!"
Right, define scientist first because a doctorate in theology from the theological university of theology doesn't qualify you as a scientist, much less an evolutionary biologist.
Furthermore the few who do disagree with the theory are extremely rare, there was a letter signed by some 200 people once which was meant to be those who were against evolution, investigation showed the majority were not actually aware of this. If I recall correctly after the investigation only a few names, literally, remained. The rest had no claim to scientific knowledge or were pure misled as to the thing they were signing.
There are numerate others but suffice to say I'm not doing them all. I will address any I see in this thread from here on out though. I will NOT provide further evidence for evolution unless I feel I should, there is a fair bit here and if you want to know the facts you should read a book by an expert.
tl;dr if this is too long for you then you have no grounds to argue about evolution. I mean that honestly. If you want to talk about how evolution is wrong I expect you to have a basic grounding in the theory itself. This covers a few common arguments from both sides, it's worth a quick browse and apologies but I don't know how to make the spaces larger to make it easier to sift through.