I can't seem to figure out how to apply both an Umlaut (¨) and the Grave (`) to the the letter 'u'. I'll type one, then the other, then the letter, but only the latter accent is applied, with the former just left out to dry. Any ideas?
There are basically two kinds of Unicode characters with diacritics:
Key combinations like ⌥u just enter a dead key state where the next key press inserts some precomposed character. ⌥⇧u would insert a combining diaresis that in turn could be followed by another combining character.
Some precomposed characters with multiple diacritics on the U.S. Extended layout: