While there are a variety of ways to input special characters not found on your keyboard, the compose key provides one of the easiest. The key sequences are fairly mnemonic, making them easier to remember, and they are often shorter than equivalent hex codes and easier to use than copy and paste. But in order to use these, you may first have to make sure your system is set up to use a compose key.
In KDE, pull up your System Settings and select Input Devices. Under the Keyboard section, select the Advanced tab and check the Configure keyboard options box. Click the arrow to expand the Compose key position section, and then check the box for the key you wish to use. I’m using the right win key, which on my keyboard is actually the Tux key.
In Gnome, pull up your System Settings and select Keyboard. Under the Typing tab, select Layout Settings. Then, under the Layouts tab select the Options... button. Under Compose key position, select the key you want to use as the compose key. Again, I’m using the right win key, which is actually the Tux key on my keyboard.
Now that your desktop environment is configured to use the compose key, all you have to do is hold down the compose key while typing the key sequence for the character you want to type. Note that some of these characters—such as the caret, tilde, and double quotes— require the shift key. You can press and release the shift key as needed while holding the compose key.
Accents and Diacritics
You don't really have to memorize the combinations for each accented character, there is generally a character for each accent, so you simply type [compose key] + [accent character] + [letter]. For instance, you use a single quote for an acute accent, so on my system Tux + ' + e gives me the accented characters for typing “résumé”.
|diaeresis or umlaut||"||ä|
|curly double quotes||<" and >"||“ and ”|
|curly single quotes||<' and >'||‘ and ’|
The right single quote character is also the preferred character for an apostrophe. The en dash is used to indicate a range of values, and for attributive compounds; the em dash is used to indicate a break in thought or interruption of speech, and to set off the attribution of a quote. Wikipedia has more information on dashes, if you are uncertain which to use.