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Wiring your model railroad can be difficult.  In fact it is the area which gives most newcomers to the hobby the most problems.  One reason is that most of us are less familiar with the details of electrical and electronics than mechanical components. But if you start with a relatively simple layout it shouldn't be too difficult.  Fortunately there are numerous reference books that can help.

The first component needed is a power supply commonly called a power pack for DC powered layouts and a transformer for AC power.  There are lots of options and we don't discuss them further here.  See Wiring Basics on the NMRA Beginners website.

You've probably noticed that most model railroad layouts have track with two rails just like real railroads.  Two rail layouts are almost always powered by direct current (DC).  DC is simpler to understand: one rail is positive and the other is negative.

But notice what happens in a reversing loop where a train changes direction: to keep a train going forward the positve rail must become the negative rail and vice-versa so the polarity must be switched with an electrical switch.  Electronics can offer an automatic solution.  Polarity problems also exist where the rails in a track switch cross each other (called the "frog").  The simplest solution is to insulate the whole frog (some switches provide this) but all locomotives must have amply spaced electrical pickups (the wheels) in order to bridge the insulated gap or the train will stop.

3 rail AC powered layouts avoid the polarity problems because both outside rails can be connected together.  But the third middle rail must have gaps at track switches so once again there is an issue with electrical pickup spacing.  Most 3 rail equipment that needs electrical power has a sliding or rolling contact on the middle of the underside and can be spaced at opposite ends of the loco or car and is usually sufficient to bridge any third rail gaps.

In the past few years electronics have become more common in model railroading.  Perhaps the greatest advance is Digital Command Control (DCC).  DCC replaces control of model trains by adjusting the voltage by sending digital commands from a hand held or wireless control module to the model railroad via the track or through the air.  Note that a wireless controller likely will still operate the trains via commands sent through the track.  A good reference is the NMRA DCC Home Page.

Another electronics advance is sound systems.  Today your model railroad locomotive can sound like the real thing due to sophisticated electronics.  Sound systems are usually associated with DCC (although not strictly necessary) so much of the information about sound systems can be found at DCC referencces.

Additional electrical issues not covered here include on board components, signaling, passenger car interior lighting and electrical scenery elements.

References:
http://www.building-your-model-railroad.com/model-railroad-wiring.html
http://www.model-train-tips.com/blog/1205/dc-control-wiring-basics-for-your-model-railroad/
http://www.ehow.com/how_7887677_lionel-transformers-instructions.html
https://secure.wikimedia.org/wikipedia/en/wiki/Digital_Command_Control

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