Using umlauts more quickly
I'm sure this isn't new to many of you, but if you are using a flavor of Linux (I'm sure you can do something similar in other OS's), you can turn the 'compose' key on in your layout options to easily apply umlauts to characters and even type ß.
To apply an umlaut, first press the compose key, then shift+quote, and finally the vowel for which to apply the umlaut. For ß, just press the compose key and then the 's' key twice. Once you get used to the shortcuts, you can really pound out ¨'s and ß's quickly.
If you don't have a fancy gnome setup you can set the compose key option in xorg.conf: "XkbOptions" "compose:rwin".
In windows the functionality is standard, left CTRL is the compose key. The only difference is that you should hold down the compose key while pressing the modifier (^ or " or / etc). You can't do ß in windows because CTRL-s is hotkey for save.