Whenever possible, shops use prefabricated panels of copper-clad laminate material they purchase from suppliers. 

Shelves at Royal Circuit Solutions in Hollister, California are stocked with various copper-clad cores

These panels are typically 12"x18", 18"x24", or 24"x36" in size. Entire panels must be fabricated as a single unit - so to save costs, engineers will often order multiple projects or multiple copies of a single project on the same panel.

This panel is coming out of an electroplating tank -- it shows 12 copies of a board on a single panel.

One way to save money in a design is to ask your fabricator if you can split your panel with another customer. In fact, entire companies such as OshPark have been built on this model.

This image shows multiple customer designs on a single panel.  The photograph is from https://twitter.com/oshpark

Copper Weight

The foil that is used on a PCB comes in several standard copper weights with 0.25 oz, 0.5 oz, and 1 oz used most frequently in standard PCB designs.  Heavy copper refers to 1.5 oz or greater.  Most shops keep up to 3 oz copper weight on hand.  Royal Circuits keeps 4 oz and some 6 oz on hand.  Heavier copper weights must be ordered from a supplier, which adds at least one day to a PCB order.

Electroplating increases the copper thickness of every board.  So a board made with 0.5 oz copper that is electroplated with an additional 0.5 oz, will end up with 1 oz of copper on the outer layers.

Dielectric Selection

Between the layers of copper foil is a dielectric material with specific material properties.  The IPC-4101 standard details the various property requirements of these dielectrics and engineers often refer to slash-sheets, an appendix to the standard.  For your first projects, you'll likely only ever use FR-4 (Fire-Retardant Level 4) materials -- they are the cheapest and most ubiquitous dielectrics in use today.  But if you are designing an RF circuit, you should work with your design-house to investigate more suitable materials.