If you don’t want to remember the sometimes-obscure key combination required for each diacritical, you can use Mac OS X’s Keyboard Viewer to figure out which combination does what, but it’s a bit of a hassle to have to show and hide Keyboard Viewer each time you want a special character.
For example, to get ä, you type Option-u and then type a.
Long-time Mac users know that you can type diacritical characters-for example, â, é, ì, ü, and ñ-by first typing the diacritical (which usually requires the use of the Option key) and then typing the letter.