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.

Here is an answer close to 1st answer, with a little alternative: I do not need to use compose because I set my keyboard to English US international instead of English US or English UK.

So I use the following combo:
" then e for ë
' then e for é
` then e for è
` then a for à
~ then n for ñ

and
" then spaceBar for "
' then spaceBar for '
` then spaceBar for `
~ then spaceBar for ~
Alt Gr plus 5 for €

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.

Note for dummies like myself. It took me a while...

1. Press Cont & Shift & u together
2. Let go of all three keys
3. input code (for example: 00e1 for á)
4. Enter