Throwing piece-by-piece
The piece-by-piece approach is probably the most common way to throw on the wheel. You start out with an idea of the finished product in mind, and weigh out a block of clay to the amount you need. Next, you wedge the clay and throw it on the wheel to give it the shape you had in mind, before lifting it off and starting on the next piece.
When I work this way, I try to throw the object with thin walls in order to minimise the trimming process. I also give the outside of the object more attention and try to get the shape as close to the finished product as possible, since major flaws in the walls can't be corrected as easily. Unlike my throwing-from-the-hump approach, I mostly don't burnish the inside, but instead leave the marks my fingers left behind in the process of pulling up the walls. There are exceptions, though, like bowls, for example, where a smooth inside is critical.