Push/Pull To Delete

I’m a new user and am having problems using the push/pull tool. Totally my issue, but I could use some help. I want to use the push/pull tool to delete from a surface – essentially create a hole in 3d rectangle. I’ve been successful but only by accident. What is the trick? Some tutorial videos talk about doing the extrude and dragging off into space will delete, but I cannot make this work. Any help would be great.

You drag it to line up with the other surface.

IOW, push/pull until you go to the opposite face and it says “On Face” or “On Edge” as @Box did.