OS X has a few useful built-in correction and substitution functions that you can use when composing documents in various applications. One of these is the option to check spelling as you type, which has been around for a while, but more recently Apple has introduced system-wide character substitution and word suggestion options. While these options are available to applications, they will only work for those coded to take advantage of them. These include Apple's iWork and iLife programs, as well as TextEdit and Safari, but other third-party programs also support these services.
Spell-check as you type
OS X offers a system-wide spell-checker that can be set to dynamically check spelling as you type. For applications that support this, the settings for the spell-checker are usually available in the "Edit" menu under "Spelling and Grammar," and can be set to check spelling as you type, or to check it on demand. Misspelled words will be underlined with a red dashed line, and suggestions for correct spelling will be available if you right-click the word.
Along with spell-checking, Apple has included a grammar check routine; however, this is a rather rudimentary implementation and does not catch many grammatical errors and sometimes offers incorrect advice. Nevertheless, it is available in the same menu as the spell-checker and can catch some errors.
In OS X Snow Leopard, Apple introduced text substitution. While for the most part it is used for symbols, it can also be used for word substitution. Apple includes a number of default options, such as copyright and trademark symbols, but provides the option to add customized words and other substitutions of your choosing. To set this up, go to the "Language & Text" system preferences, and in the "Text" tab, use the plus button to add new substitution options. In order to use symbols, glyphs, or other nonstandard characters in the substitution, when you are entering the replacement text it might be useful to have the system's "Character Viewer" panel open (available from the input menu) so you can insert desired symbols.
One additional composition aid that is available in Snow Leopard is word suggestion, which can be used in part as an autocompletion feature. To invoke it, just start typing a word and press escape. Applications that support this feature will display a list of words that start with the entered text, and then highlight a suggestion. You can then use arrows to select from the list, or continue entering characters, and when the desired word is highlighted, pressing either the "Tab" or "Enter" keys will complete the word.