There are a number of techniques for producing a circuit board.  The most prominent methods are:

1. Acid etching

The most common method, used for everything from high-volume industrial to hobbyist board production. A circuit design is applied to a copper-coated board using acid-resistant material.

Two techniques are popular here; developing of photosensitive board stock, or toner transfer methods. Acid is used to dissolve the exposed copper, leaving only copper in the desired design. DIY PCB Etching Tutorial

2. Copper removal

Similar to the etching process, there are a few techniques that involve selectively removing copper from a plated board.  The most common alternatives to etching are based on either mechanical CNC milling and routing of traces, and the use of high-powered lasers to remove copper by ablation.

3. Deposition

General name for a variety of techniques that add copper to a board to build up the circuit.  Some approaches are based on electroplating while others focus on using conductive ink to create circuit traces.

Deposition techniques have some shortcomings however; the conductive ink used to print circuits is more easily damaged than traditional traces, and electroplating methods are very complex.

No matter the technique used to create the circuit traces, a few steps remain before the PCB is ready for use.  Final finishing may include drilling of component or mounting holes, milling of the board outline, or the application of a silkscreen or solder mask.