Step 1: Components
There are many types of component that are important when building circuits such as LEDs, capacitors and transistors. All of these components are available at RadioShack or other stores and they are key components for a beginner.
555 Timer - An IC used to provide time delays, such as an oscillator and other applications.
555 Timer @ RadioShack
Batteries - Stores chemical energy for transformation into electrical energy.
Batteries @ RadioShack
Capacitors - Used to store energy in an electric field. They come as electrolytic and ceramic variants.
Sunrise Alarm Clock
Capacitors @ RadioShack
LEDs - (Light-Emitting Diode) A semiconductor light source.
LEDs @ RadioShack
Resistors - Implements electrical resistance as a circuit element. These are often used with LEDs.
Resistors @ RadioShack
I found this useful when making large LED arrays: http://led.linear1.org/led.wiz
Voltage Regulator - Electrical regulator designed to automatically maintain a constant voltage throughout a circuit. A specific type of transistor.
USB iPhone Charger
5V Voltage Regulator @ RadioShack
Wire - Metal strands used to carry electrical current.
Wire @ RadioShack
Switch - Able to break electrical circuit.
Switches @ RadioShack
Transistor - Semiconductor used to amplify and switch electronic signals.
Transistors @ RadioShack