How did you make the image in the introduction to the website, with the models and cutaway view into the brain?

To make models such as the skin and brain in the tutorial, you can use two modules on the Slicer Main menu: Editor followed by ModelMaker. Also, see the User's Guide, under Segmentation.

To display the cut-through, you will need to use the Clipping functions in Slicer.
First, you can display the models and grayscale slices that you are interested in.
Then click the Display tab on the Models panel, and right-click the model that you want clipped. This should be the skin model if you are using the tutorial data from the ftp site, for example.
A menu will appear. Select Clipping to turn this on. Now the model will be cut by the grayscale slices.
Next, click the Clip tab on the Models panel to adjust which side of each grayscale slice should be used to clip the model.

Finally, to remove the black background in each of the grayscale slices, you may use thresholding.
On the Display tab of the Volumes panel, there is a Threshold function.
Click Auto and the black background should disappear. You may also manually adjust the thresholding to get the desired effect.