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Before other things, you should understand (and eventually clarify here) what is the role of PieChartWriter class.

I can think two possibilities:

a) PieChartWriter is a simple "bean" class,...

Ok, now the graphics appearance is clear. What are your further problems/questions? Are you able to create a JFrame that contains a panel in which you draw, for example, an initial circle?
I can't...

Ok, and how much do you know about Swing, components and custom painting?
And are you sure that your PieChartWriter should have methods like setSlice1, setSlice2 etc..? In other words with the pie...

Obviously, I know what is a "pie chart". The question is: do you need to generate an image file (e.g. png)? Or do you need to show the pie chart in a window? Or other?

Personally, I don't have that book ... and I don't know what is the PieChartWriter.
So, what's your problem/question?