Multilayer PCBs are only a little different that the Double Sided PCBs.
Multi Layer PCB Stackup As you can see in the image to the right, a four-layer board starts with a rigid core of FR4 and copper. The internal core is processed for traces on those prior to the other fiberglass and copper being added, and the entire board is laminated together.
Multi-layer pcb
There is the B stage PrePreg, which is fiberglass that is still soft that will need to be heated in order to become rigid. It acts like a glue to keep the inner core adhered to the outer copper foil.
The copper foil added consists of very thin and loose sheets of copper. They are sandwiched together with the Prepreg and inner core, and placed in a PCB Lamination Press. Pressure and heat are applied to the material, which causes the Prepreg to "flow" and bind the layers together. Once it cools, the fiberglass is then hard and the entire board is very rigid.
