The dative case
German marks the indirect object — the person you give something to, help, or thank — with the dative case. The articles change again: nominative der/die/das/die become dative dem/der/dem/den, and plural nouns add an -n to themselves on top of that. The dative is also triggered by a fixed list of verbs (helfen, danken, gefallen) and a fixed list of prepositions (aus, bei, mit, nach, seit, von, zu) — once you know the lists, the rest is mechanical.
The article table
Nominative → accusative → dative. Masculine: der → den → dem. Feminine: die → die → der. Neuter: das → das → dem. Plural: die → die → den + -n on the noun. So die Kinder (the children) becomes den Kindern in the dative — note the extra -n on Kindern, on top of the article change. Indefinite: ein → einen → einem (m./n.), eine → eine → einer (f.). Possessives follow ein: mein → meinen → meinem (m./n.), meine → meine → meiner (f.), meine → meine → meinen (pl., plus -n on the noun).
Indirect objects: 'to whom?'
When a verb has both a direct object (the thing) and an indirect object (the person), the person goes in the dative. Ich gebe dem Mann das Buch. = 'I'm giving the man the book.' = 'I'm giving the book TO the man.' The dative noun usually comes BEFORE the accusative when both are nouns. Ich schreibe meiner Mutter einen Brief. = 'I'm writing my mother a letter.' Common verbs that take both: geben (to give), schreiben (to write), schenken (to give as a gift), zeigen (to show), sagen (to say to).
Dative-only verbs
Some verbs take a dative object even when there's only one object — there's no second 'thing'. The big three at A1 are helfen (to help), danken (to thank), and gefallen (to please / to like). Ich helfe dem Mann. = 'I help the man.' Ich danke dir. = 'I thank you.' Das Buch gefällt mir. = 'I like the book' (literally 'the book pleases me'). Just memorize them as 'dative verbs'.
The seven dative prepositions
Memorize the chant: aus, bei, mit, nach, seit, von, zu. Anything that follows one of these is automatically dative. aus dem Haus (out of the house), bei meiner Mutter (at my mother's place), mit dem Hund (with the dog), nach der Schule (after school), seit einem Jahr (for a year — and still going), von dem Vater (from the father), zu dem Bahnhof (to the train station). Two contractions you'll see everywhere: zu dem → zum, zu der → zur, bei dem → beim, von dem → vom.
Personal pronouns in the dative
The pronouns also have dative forms: mir (to me), dir (to you informal), ihm (to him / it m./n.), ihr (to her), uns (to us), euch (to you all), ihnen (to them), Ihnen (to you formal, capitalized). Er gibt mir das Buch. = 'He's giving me the book.' Ich helfe dir. = 'I'll help you.' Wie geht es dir? — that dir you've been saying since lesson 2 is a dative pronoun!
