First of all, those two dots are the vestiges of a medium-old-fashioned way to write the letter e on top of a vowel —pretty similar as Swedish and Danish do it with the little o on top of the letter å— In much older German texts, you will actually find a small e printed on top of another vowel.
And that pretty much explains what Umlaute are. They are a special kind of Ablaut, involving the vowels a, o , u and the vowel e.
das Kaufhaus, die Kaufhäuser
The letter combination au is a Dipthong which sounds similar to the sound English writes as ow. It's ablauted partner is äu, and that's it. German has some more Dipthonge, but au/äu is the only one involving an Umlaut. Äu sounds just the same as eu (English writes this sound oi or oy.)
That's the one exceptional case. The general rule for doing the Ablaut (for plural, past tense, downsizing, etc.), however, is
- put the Ablaut on the last non-reduction syllable of the last component, ignoring suffixes and case/tense endings.
Often enough, this is just the first syllable of the last component, ignoring prefixes. This explains why it's
Es ist sechs Uhr morgens. Die Kaufhäuser sind noch geschlossen.
Auf dem Wochenmarkt wird schon gekauft und verkauft.
Käufer und Verkäufer feilschen um die Preise.
An ihrem Verkaufsstand bieten die Obstverkäuferinnen auch Gemüse an.
An den anderen Verkaufsständen gibt es Wurst und Käse.
The last component of Obstverkäuferinnen is Verkäuferinnen, the plural nominative ending is -nen, the female occupation suffix is -in-, the actor suffix is -er-. The syllable to put the Ablaut on is kauf. And as that's the au Dipthong, it gets äu.
Important note: This rule only explains where to put the Ablaut, but not if it has to be put there or not. The latter depends on a lot of factors. As a language learner, you better stick to learning
- the gender (always recap the nominative singular der/die/das along each word)
- the nominative singular
- the genitive singular
- the nominative plural
This is what a dictionary gives you for each noun. It's the only information you need to put the noun into one of the patterns which you will learn automatically as soon you are sufficiently exposed to German.