I've looked all over the internet, but I couldn't find anything. The only tutorial I could find about this was made in 2013, so it was a much earlier version of Blender that I couldn't follow along with. I started using Blender yesterday. Any help is greatly appreciated, thank you!
Select the object that will be the "hole" in the 2nd object,
Shift + select the target object.
Tab to enter edit mode
Numpad 7 to go to top view (the cut will be projected so the view is important).
Enter edit mode with both selected, go to mesh, knife project.
Then just remove the resulting face.