Hold Option + u, produces an ¨ that's got a yellow background. If you then type another letter after it (ä, ü, ö (or even ï, ë, or ÿ)), it will produce the letter with an umlaut over it.
Also, to produce a ß, just press Option + s.
In addition to umlauts, you can also use acute accents (´) by using Option + e, a grave accent (`) by using Option + `, and circumflex accents () by using Option + i, all in the same way the umlauts are used.
Easiest way I've found so far, anyways.
PS: This works in any Mac program (Safari, Word, Pages, etc.)