Cut a hole with the Elliptical Marquee tool

Digital Scrapbooking Primer: Cut your Paper

Select the paper you want to cut with the move tool
Select the Elliptical Marquee tool
Create a selection in the shape of the hole you want to create
Press Delete
Go to the Select menu, then Deselect (or press Ctrl+D, Cmd+D on a Mac) to deselect the marquee