Chinese characters are composed of what are known as strokes. A stroke is what is drawn by the brush or pen in a single movement, until the pen is lifted off the paper. Strokes are often combined to form pictures or to form pieces of pictures.
These pieces are known in Chinese as 部首, pronounced bùshǒu. In English, they are usually called radicals. Radical is a word that has the same origin as root, as these form the pieces of the pictures that compose characters.
Traditionally, there are considered to be 214 radicals, on the basis of the original list compiled during the reign of the Qing dynasty emperor Kangxi. Some of these radicals are themselves complete characters, while others are only parts of characters.
Some radicals always appear on the left side of the character, others on the right side, others on the top, and others on the bottom. Some can appear in more than one position. Others fully or partially enclose the rest of the character.
Some radicals are easy to identify, while others can be confusing due to similarity with others or difficulty in recognizing which radical is fundamental.
There are numerous sites on the Internet that list these radicals. The web page http://en.wiktionary.org/wiki/Index:Chinese_radical lists the radicals in traditional order, beginning with the simpler radicals and progressing toward the more complex radicals. Wikipedia also has a useful list, at http://en.wikipedia.org/wiki/Kangxi_radical.
The below table was taken from the wikipedia page:
There is a very nice version of this list at Wikimedia, which shows the evolution of the various radicals, at:
http://commons.wikimedia.org/
wiki/Commons:Ancient_Chinese_characters:214_radicals