Umlauts aren't important, right? They are just ornaments on top of the letter, right?

Wrong, and wrong. Umlauts are important. Letters with umlauts are different letters. The letter ü is not a u. They're as different as if the were p and q. They are pronounced differently.

Düssel is a river that runs into the Rhein. A Dussel is an idiot. So, Düsseldorf is a village on the Düssel river; Dusseldorf is a village of idiots.

It used to be that if you input "Fussen" on the Bahn website, it would give you Fussen Strasse, somewhere in northern Germany. Now they included an ignorance alorithm that tries to figure out what you really mean, and offers Füssen.

In many cases you can just add an 'e' after the vowel (ue for ü), and there is some historical justification for doing this. Websites like the Bahn will accept this spelling.

Other website, however, like the Bahn Ticket Shop, demand exact spelling. If you want a Bayern-Böhmen-Ticket, you have to put in Bayern-Böhmen-Ticket, Bayern-Boehmen-Ticket doesn't work.

So, how do you make an umlauted character without a German keyboard? You use the "alt" codes. Hold down the Alt key and type one of the numbers below on the numeric keypad (not the numbers across the top of the letters on a regular keyboard).

The numbers are:

Ä	0196
Ö	0214
Ü	0220
ä	0228
ö	0246
ü	0252

The leading zero is important.