Capacitor
What they look like:

How they are shown on circuit diagrams

Their purpose
Capacitors are short-term electricity storage devices. Storing electricity in a circuit has a number purposes including:
How to identify them
Capacitor values are measured in FARADs - F
The greater the value of capacitance, the more electricity the capacitor can hold ie. a 1 F capacitor will store 10 times the electricity of a 0.1 F capacitor.
Values of capacitance can vary from pico Farads (one millionth of a millionth of a Farad) to micro Farads (one thousandth of a Farad) or larger. Due to the small size a knowledge of Scientific Notation is handy.
pico Farad 0.000000000001 Farad or pF
nano Farad 0.000000001 Farad or nF
micro Farad 0.000001 Farad or uF
In general, capacitors are identified in two ways:
1. By clear labelling of the value in Farads and maximum voltage
This is typically used for electrolytic and tag tantalum capacitors will clearly shoe a value in Farads and a voltage ie:
10uF 16V
Which indicates a capacitance value of 10 micro Farads and a maximum voltage of 16 Volts
2. A code system which typically applies to greencaps and ceramics. In this study we are only interested in the first three numbers of the code which indicates the value of the capacitor in pico Farads (pF). In general you will see three digits at the start of the code. The first two digits represent the first two digits of the value (in pF) and the third digit is the number of zeros.
For example
A capacitor marked with 103 = 1 0 000 pF (ten thousand pico Farads)
OR 10 nF OR 0.01 uF)
A capacitor marked with 121 = 1 2 0 pF (one hundred and twenty pico Farads)
OR 0.12 nF
Combination of Capacitors
Resistors can be connected in two ways, serial and parallel:
Serial

In the above schematic, two capacitors are connected in serial (one after the other) fashion at point B. The total capacitance measured from A to C is given by the formula:

Any number of capacitors can be connected in this way ie. the total capacitance is given by...Cn (where n is the number of capicitors).

Parallel

In the above schematic, two capicitors are connected in parallel (side by side) fashion at points A & B. The total capacitance measured from A to B is the sum of the two capacitors.

Any number of capacitors can be connected in this way ie. the total capacitance is:

Cn (where n is the number of Capicitors).