Most special characters are added through a combination of keystrokes - usually holding down the Alt key while typing a series of numbers on the number pad on the right side of the keyboard. Washington State University and Penn State have some great resources. Make sure you are looking at the information for Windows or Mac, as appropriate!
What kinds of characters can you add? Just about anything! Greek letters (π Ω ø ∆ ∂), foreign characters (œ æ £), mathematical symbols (∞ ≈ ≥ ÷ ∫), physical units (㎨ ㎲ ㎒) and plenty of other characters.
It is not recommended that you copy and paste special characters onto your site from another program. The published results may not be accurate. In this blog post, the font size of the special characters has been increased to make them easier to read, since they often appear rather small as compared to the main body of text.
Enjoy the added functionality that these special characters afford you!