When you create a new document, go to where it says Preset and in the pulldown window, select Custom.

Then in Width set it for the number of inches wide your notebook cover is and be sure to use the pulldown to set it to inches, not pixels or centimeters or anything else. Do the Height setting the same way. Under resolution, you should be fine setting it for 200 pixels/inch. Sometimes for print you would go 300, but for printing at home 200 should be fine.

I could explain all the details of changing a document's size, but you are much better off with starting with the right size document to begin with. It sounds like you are starting from scratch, so you should be fine.

Export your Illustrator files as a wmf or emf (windows/enhanced meta file). They are both vector image formats and should work in publisher.

Alternatively, you can directly copy (ctrl C) what you want from your illustrator file and past it (ctrl V) into your publisher document.

I've found that by using the select tool and then going to edit-cut works best for me. The selection tools offers more control and there are three different ways to select the area in the image you want to crop; square, circle, and free-form (or poly).