Richard Dawkins in one of his videos says that Evolution is a fact and not just a theory.

He goes on to say that man and chimpanzees both evolve from apes.
Is this correct (Is evolution a fact and did humans & chimps evolve from apes)?

A tiny bit of terminology

Fact


In popular culture, the term fact means "something that is true". I would consider a theory as being the closest concept in science to what is called a fact in the population culture.
In natural sciences, the term fact is rarely used but would have the same meaning than the one in popular culture. The reason we are not often using this concept is that in science (nor in any other field of knowledge) one can never definitely know the truth. We can only have evidence that are congruent with a hypothesis or body of statements. In such case we talk about theory (see below).


Theory


In popular culture, "theory" is used to mean what the natural sciences call a "hypothesis."
In the natural sciences, a theory is a body of thoughts/statements that is very well supported by loads of evidence. In science, a theory is not a hypothesis. For example: Theory of evolution, Theory of general relativity, transition state theory, etc. Note by the way that various definitions of theory are in use (ref.). The below answer respects the definition that I gave above.


The scientific terminology presented above is actually a matter of philosophy and not science. If you need more information about the definitions of "theory", "fact" and other related terms, you may want to ask on Philosophy.SE. Stephen Jay Gould summarized the concepts of theory and facts nicely when saying


  [..] facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts.


In the answer below, I am using the scientific terminology.

Your questions


  Is evolution true?


Evolution is what is called a theory in natural science (The Theory of Evolution a.k.a. modern evolutionary synthesis), and it is extremely well-supported. Evolution is NOT a hypothesis. In other words, we have a lot of supporting evidence that living beings have evolved and are evolving.


  Did both humans and chimpanzees evolve from apes?


Humans and chimpanzees are apes (great apes to be more accurate). Both humans and chimpanzees evolved (and are still evolving) from a common ancestor who already was a great ape. We have a lot of evidence to support this common ancestry.

What does the theory of evolution say?

Understanding Evolution (by UC Berkeley) is a short and introductory course to evolutionary biology. Of course, there exist other good sources of information online such as Evolution and the tree of life by Khan Academy.

We have a number of posts providing book recommendations for 


General biology (Books for beginners and Introductory biology text for an outsider)
Intro to evolutionary biology (Text Book Recommendation: Organic Evolution and Introductory books about evolution)
Intro to evolutionary genetics (Books on population or evolutionary genetics?)


You will also find a lot of introductory posts on biology.SE such as for examples:


Why do some bad traits evolve, and good ones don't?
Is there a biological mechanism for evolution encoded into our DNA?
Does it make sense to classify all humans in a single species?
Why is a heritability coefficient not an index of how “genetic” something is?
How could humans have interbred with Neanderthals if we're a different species?
If dinosaurs could have feathers, would they still be reptiles?
Why does evolution not make our life longer?
Why don't mammals have more than 4 limbs?
How to define “evolution”?
How did some humans evolve to be white?
Who are humans' closest relatives, after primates?
Did cats evolve from monkeys ? or vice versa?
Why do the ancestors of birds still exist?
How does Natural Selection shape Genetic Variation?


What are the evidence?

Demonstrable and repeatable examples of evolution lists sources that list evidence. There are probably thousands of pieces of evidence listed in total, all explained in lay terms with links to the original article. Of course, this is just a small sample of the evidence we have.

The post Is there any biological evidence that is not suggestive of or seems to disprove evolution? might be of interest too.



Thanks to @CortAmmon's comment for correcting a very poorly phrased sentence.
