While holding down the "Alt" key, type in the following numbers.
Once you have typed in the number, release the "Alt" key.
Your selected German character should appear.
Be sure that you type the numbers using the numeric keypad.
The numbers on the "! @ # $" etc. keys will not access these characters.
Be sure that the "Num Lock" light on your keyboard is lit.

 

Ä	= 142	Ö	= 153	Ü	= 154
ä	= 132	ö	= 148	ü	= 129
				ß	= 225

To access the umlauted vowels (ö, ü, ä) use the following keyboard shortcuts.
Hold down the "ctrl" and "shift" keys then hit  " ; "  (semicolon).
Let up on all keys, then type the vowel you want.
If you want upper case:
Hold down the "ctrl" and "shift" keys, then hit  " ; " (semicolon), then hit the vowel key.
When you let up on the keys, the upper case vowel will appear.
To access the "ß", hold the the "ctrl" and "shift" keys then hit  "&".
Let up on all keys, then type "s".

Hold the "option" key then hit "u."
Let up on both keys, then type the vowel you want.
To access the "ß," hold the option key, then hit the "s" key.