For a basic introduction, please read Apple's Mac OS X 10.2: About Languages and Input Methods article. Admittedly, this is a pretty cursory overview and description, but it's a good place to start if you are unfamiliar with this part of the Mac OS.
Keyboard layouts, input methods and the Input Meu (aka Keyboard Menu) have been part of the Mac OS for a very long time (System 7.1 era, circa 1994). Still, many North American Macintosh users have never had any experience with this part of the Mac OS.
If you're currently running Mac OS X 10.3 (Panther), there is an overview entitled "About keyboard layouts and input methods" in Mac Help (this item is not in the Mac Help for OS X 10.2). Search for the 'input methods' in Mac Help to read this particular topic.
About keyboard layouts and input methods
From Mac Help, Copyright Apple Computer, Inc.
You can write in languages that use a different writing system (or "script") from yours without having the physical keyboard that's designed for that language. To write in a different language, you need to select the "keyboard layout" or "input method" in International preferences, and then choose that keyboard layout or input method from the input menu when you're ready to type.
A keyboard layout determines what characters appear when you press a key on your keyboard. The layout of keys on an Italian keyboard, for example, is slightly different from the organization of a U.S. keyboard. If you are more familiar with Italian keyboards, you can use the Italian "keyboard layout" with your U.S. keyboard, allowing you to type as if you had an Italian keyboard.
The input method also determines what characters appear when you type, but additionally provides a way to choose between alternative characters. This is important for some non-Roman languages like Japanese or Korean which have too many characters to fit on a physical keyboard. When you type a sequence of keys that refers to more than one character or word in a script, a window appears allowing you to choose the character or word you want to use.
When you're ready to type in another language, you choose the keyboard layout or input method for that language from the input menu (which looks like a flag or alphabetical character) on the right side of the menu bar. You'll need to know what keys to press in order to see the right characters appear on your screen. If you aren't familiar with the selected keyboard layout, you can use the Keyboard Viewer to show you.
To get some idea of the history:
Useful Hints and Tips
There are some useful keyboard shortcuts defined by Mac OS X for switching between keyboard layouts and input methods. Open System Preferences, International, Input Menu tab. Click the Options... button. We recommend that the "Use Command+Option+Space to rotate to the next keyboard layour or input method in the active script" checkbox is checked (this is the default setting). When checked, you can type command-option-space to rotate between Spell Catcher and your keyboard layout.
Turn on the "Character Palette" item in System Preferences, International, Input Menu tab. Try it out - it's very cool and quite useful. If you're currently running Mac OS X, Find out more about the Character Palette in Mac OS X Help.