How can I type accented characters like ë?

Often this is easier with the compose key. With that configured you use key combos to get the special characters. For instance:

• For ë you press Compose+", e.
• For ẽ you press Compose+~, e.
• For ô you press Compose+^, o.
• For á you press Compose+', a.
• For à you press Compose+`, a.
• For € you press Compose+=, e.
• For £ you press Compose+-, l.

Note that you do not have to hold down the compose key; just press each key in order.

To set the compose key go to System -> Preferences -> Keyboard, then Layouts -> Options. Open up Compose Key Position and choose a key. I use Right-Alt.

If you know the unicode value of the character you'd like to type, hit CTRL+SHIFT+u and then type the unicode.

Example:

CTRL+SHIFT+u 0 3 b b ENTER

results in λ.

The easiest way I've found to do this is to set your keyboard layout to USA International (AltGr dead keys), then use Right-Alt+whatever to get the character you want. Obviously this does not work for all international/special characters, so if you need one that's not available through this method, use one of the other methods listed here.

Wikipedia gives us a handy diagram of the available characters and the keys they are mapped to.