Dativ.
Who receives the action?

The Dativ is the recipient. Not the doer → Nominativ, not the target → Akkusativ. The one the action goes to or happens for.

Also: The Dativ builds on Nominativ and Akkusativ. See German Nominativ Case and German Akkusativ Case.

The question that finds the recipient

After the verb, ask → Wem? "To whom? For whom?" Whatever answers that question is Dativ. It's the person receiving: the one who benefits, gets something, or is indirectly affected.

• Ich gebedemManndasBuch. Give to whom? demMann. → Dativ.
• Sie schreibtderFraueineNachricht. Writes to whom? derFrau. → Dativ.
• Er kauftdemKindeinEis. Buys for whom? demKind. → Dativ.

Three colors. Nominativ is always the doer. Akkusativ is always what gets acted upon. Dativ is always the recipient. In a full sentence you can read the grammar off the colors before you parse a single ending.

What Dativ does to articles

This is where German makes a bigger move than the Akkusativ did. Every gender changes in the Dativ, and masculine and neuter land on the same form → dem.

Gender	Nominativ	Dativ
Masculine	der / ein	dem / einem
Feminine	die / eine	der / einer
Neuter	das / ein	dem / einem
Plural	die	den (+n)

Notice: feminine Dativ uses der, the same form as masculine Nominativ. Context tells them apart. And masculine and neuter share dem, so there are really only two new forms to learn → dem and der.

The plural rule: add -n

Dativ plural has one extra rule: the noun itself picks up an -n ending, unless the plural already ends in -n or -s.

Nominativ plural	Dativ plural
dieKinder	den Kindern
dieMänner	den Männern
dieFrauen	denFrauen (already -n)
dieAutos	denAutos (already -s)

One rule, very few exceptions. If the plural form doesn't already end in -n or -s, add one in the Dativ.

Three colors in one sentence

This is the clearest way to see how the three cases work together. Each role has its own color:

Example	Roles
Ich gebedemManndasBuch.	doer → recipient → thing
DieLehrerin erklärtdenKinderndieRegel.	doer → recipient → thing
Er zeigtseiner MutterdasFoto.	doer → recipient → thing

Fixed Dativ prepositions

A group of prepositions always takes the Dativ, no question to ask. You see them, you know the case.

Preposition	Meaning	Example
mit	with	mitdemMann
bei	at / near / with	beiderArbeit
von	from / of	vondemKind
nach	after / to (cities)	nachderSchule
seit	since / for (time)	seiteinemJahr
aus	from / out of	ausderStadt
zu	to	zu + dem → zum
gegenüber	opposite / towards	gegenüberdemBahnhof

Note → zu dem contracts to zum and zu der to zur in everyday speech. Same with von dem → vom, bei dem → beim. These contractions are not optional in spoken German. They're standard.