In the anime at least, I think kakashi explained that the sharingan allows its user to see and understand the underpinnings of any technique. So in addition to knowing the hand seals, they also know how to mold the chakra to perform the technique. So basically, any technique can be seen will be understood and therefore copied. So a technique like the rasengan that doesn't require any hand seals can also be copied, although the user would have to go through a lot of trouble to gain the chakra control and stamina needed to use it. This task would be made easier, however, by the knowledge imparted by the sharingan. That's why Sasuke was able to gain Lee's taijutsu techniques in a month or less.