Basic extrude question Just started with Blender.

I made a shape ( picture 1) Now I want to make a circle on this face and sink it into the shape.

What I do is create a circle, place it onto the original shape, press F  to give it a face, make an inset (picture 2), and then when I try to extrude (picture 3), it does not create a hole.

Probably because I have two faces on top of each other. How would you go about this?
are you looking to make a hole? try the boolean Modifier, difference, apply and remove the cilinder (and good luck with Ngons and strange things if your planes are not 100% flat).