This is just a theory, and how that theory works. Note that this only applies to the normal Sharingan. Mangekyo has just gone straight into magic.
Theory
Each Tomoe (A.K.A. little comma thing) in a sharingan eye, is a new pupil. They also have some special properties, different from normal pupils. I'll expand on this in more specific bits.
Copying
Each new pupil lets in more light, and therefore, more detail. As we already know, Sharingan copies by letting the user see an opponents hand signs, and allowing them to mimic the motions. As more detail would be let in by the new pupils, what would previously be a blur, would make each hand sign clear, and since ninja's already know the hand signs, they could simply use that order and combination of them, letting out the jutsu.
Giving color to Chakra
One of Sharingan's other abilities is too "give color to chakra", allowing them to see it. Well, the explanation here is that chakra actually gives off ultra violet light, allowing it to be seen by anything that can see that. Sharingan's extra pupils could see different colors than the normal pupil, allowing for the seeing of chakra.
Real Life Example
Human beings have binocular vision, meaning that they have one pupil in each eye.
The Mantis Shrimp has Triocular vision, meaning it has three pupils in each eye (sound familiar?). This allows them to see over 100,000 different colors (that's ten times more than humans) including Ultra violet and infrared light. They also have much greater reaction time than other crustaceans (sound familiar?), as their eyes capture more detail, quicker.
The special techniques
All special techniques unique to Sharingan come from Mangekyo.
So, I ask you all... for explaining the normal sharingan, is this theory sound?