Smart Casting is enabled by turning it on in the menu, or by holding shift and hitting your skill while mousing over your target. I personally use SHIFT as I don't always want to smart cast. Smart casting allows you to chain your abilities to have multiple abilities go off at once. Brand, Annie, Akali and others benefit significantly from smart casting. With a champ like Brand, it is possible to pop all four abilities at the same time, frequently resulting in an insta-gib.
For skill shots, point your mouse in that direction, hold shift and your hit skill shot. Learn to use some form of smart casting. Champions like Veigar benefit heavily from it.