The Curve Tool will require experimentation on your part. This page is just for some introductory ideas if you've never seen it before. But I'd suggest that the Histogram tool described in the "Simple Way" page is plenty for most of us, certainly for the first while.
The ScanWizard curve tool has two modes, Curve and Line, meaning the transfer curve can be a straight line or a smooth curve. Setting it first to Line, we can duplicate the histogram's Setting of the Black and White points, although we can't see the histogram to help us, we have to use the preview image.
Here's ScanWizard's tool in Line Mode with the end points set to mimic the histogram. We have only moved two points, but you can grab the line with the mouse and move it to many new points. Notice that the Black point is set at 15 again, and the White point is at 224, and that the remaining tones are linearly expanded over the output range of 0..255.
The point here is that this is exactly what the histogram in the "Simple Way" does and how it does it. I hope this picture makes all of the concepts more clear.