PCB etching from transparency
Stripboard

If you are starting out, I'd suggest using stripboard to start with.  

Etching PCBs

The "X-ray" is (probably) a Printed Circuit Board (PCB) design that shows where copper conductive tracks should be retained on a copper clad board which is to etched using an etchant such as Ferric Chloride.

In order to prevent the tracks being etched, a etch resist coating is applied to the copper which is destroyed by the combination of ultra-violet light and an alkali developer. Shining UV on the coated board through the transparency for a few minutes then developing it will leave the coating on the dark areas of the transparency but not on the exposed areas. You can then etch it.

There are other etchants and various ways of producing PCBs at home. Ferric Chloride is moderately nasty stuff - it will stain anything it comes into contact with and must not be flushed down drains - so disposing of used etchant can be problematic.

Here is a reasonably detailed description that includes a section on an alternative etchant that may be less problematic.



Addendum (I'm trying to find some old articles I recall reading)

Etchants


Ferric Chloride ("traditional" but nasty).
Ammonium Persulphate (see comments below)
Vinegar + hydrogen peroxide
white vinegar, hydrogen peroxide, and salt
hydrochloric acid and hydrogen peroxide


Theres a nice article on the chemistry republished at Adafruit


  it seems far better to me to
  avoid ferric chloride altogether and simply use acidified copper chloride,
  or better yet, simply start with an alternative oxidant such as hydrogen
  peroxide, and let copper accumulate in solution and eventually take over.
  An acidic copper chloride etchant can be reused indefinitely, provided that
  HCl is added periodically to provide the protons for the reoxidation
  reaction. Indeed, such an etchant solution actually improves with age!


Non-chemical methods


CNC machining.
Electrolosis)
Conductive ink (hardly worth including?)