The following is a brief introduction to sentence structure and grammatical cases, if my memory serves me well.
Sentences usually contain a verb (doing word), one or more nouns, and maybe adjectives (words that describe nouns) and adverbs (words that describe how the verb is carried out).
Here's a simple sentence:
My friend gives me the football.
Gives is the verb.
Friend is the noun that's doing the verb; it's the subject of the sentence.
Football is the noun that's having the verb done to it; it's the (direct) object of the sentence.
Me is the indirect object of the sentence.
English used to have grammatical cases but it got rid of them many centuries ago. The English case system was a lot like the one found in modern German.
Here's the simple sentence in German:
Mein Freund gibt mir den Fussball.
Gibt is the verb.
Freund is in the nominative case because it's the subject of the sentence.
Fussball is in the accusative case because it's the direct object of the sentence.
Mir is in the dative case because it's the indirect object of the sentence.
German has three genders and four cases. The genders are masculine, feminine and neuter. The fourth case is the genitive case. It's used to indicate possession, e.g. die Frau des Kritikers ('the critic's wife' or 'the wife of the critic'). Des Kritikers is in the genitive case.
From what I remember, feminine nouns don't change at all according to which case they're in. But masculine and neuter nouns do have extra endings when they're in the genitive and dative singular and in the dative plural.
E.g. Mann ('man') becomes Mannes (gen. sing.) and Manne (dat. sing.). Maenner ('men') becomes Maennern (dat. plural).
German gets worse (or better to geeks like me XD) in that the definite and indefinite articles (the, a, an), possessive pronouns (my, your, etc.) and adjectives do change with regard to cases.
Adjectives also come in two forms - 'weak' (used with the definite article) and 'strong' (used in all other instances).
This is the first paradigm I learnt. It's for the definite article, the. I must've learnt it well because I can remember it off the top of head nearly 25 years later!
masc. fem. neuter pl.
nom. der die das die
acc. den die das die
gen. des der des der
dat. dem der dem den
Of course, native German speakers and fluent speakers of German as a second language: please correct any mistakes I make.