Apple created easy ways to type non-English characters in all programs. This webpage describes most of the relevant ones for Spanish and German speakers.
For accents and umlauts, the general idea is that first you use a 2- or 3-key combination to tell the computer which symbol you want to add, and then you type the letter you want it added to. So to create a ü on a Mac, first you would press Option + u to indicate you want the umlaut as the special character, then press u again to tell it to put the umlaut on the letter u (or Shift + u for a capital Ü).
See this article for a fuller explanation of typing non-English characters on your computer.