Say you've made an illustration on an A4 sized artboard, but your illustration is a lot smaller and you want to get rid of the excess white paper. That can easily be solved.
In the example below the black stroke is the A4 paper.
1. Draw a rectangle on top of the illustration. This will be your new page size. Make sure the rectangle is selected.
2. Select the Artboard Tool (shift o) to select the A4 artboard.
3. Double click on the rectangle. The rectangle now becomes the new page size.
4. Select the rectangle with the direct selection tool and delete it. You now have an artboard (page) the same size as the rectangle.
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