In Polish we have 7 cases. I'll try to explain them using word "kot" (a cat).
"Mianownik" (Nominative) - Main case, used when we are naming something. "Jego kot jest czarny" - His cat is black. "Koty liżą masło" - Cats lick butter.
"Dopełniacz" (Genitive) - Case with really wide usage. 1) Describing possesion, 2) Using negations, 3) With some verbs. "To zabawka jej kota" - This is her cat's toy. "To nie jest wina kotów" - That's not cats fault.
"Celownik" (Dative) - Case used when describing aim of the activity, or for indirect objects. "Daję jeść kotu" - I'm feeding a cat. "Pomagamy kotom" - We are helping cats.
"Biernik" (Accusative) - Case used for direct objects. "Znalazłem kota" - I found a cat. "Widzę koty" - I see cats.
"Narzędnik" (Instrumental) - If something is an instrument of an activity, way which led for result, you should use that case. "Idę z kotem do weterynarza" - I'm going to the vet with my cat. "Psy nie lubią się z kotami" - Dogs and cats don't like each other.
"Miejscownik" (Locative) - Always with preposition. Used for describing location of an action, or when you are thinking about something. "Myślę o kocie" - I'm thinking about a cat. "Anioły żyją w kotach" - Angels are living in cats.
"Wołacz" (Vocative) - Very rare case. Used only for calling something. "O kocie, czemu to zrobiłeś" - Oh cat, why have you done that. "O wielkie koty" - Oh grand cats.
Mianownik (Nominative): kto? co? (to jest)
Dopełniacz (Genitive): kogo? czego? (nie ma)
Celownik (Dative): komu? czemu? (przyglądam się)
Biernik (Accusative): kogo? co? (widzę)
Narzędnik (Instrumental): z kim? z czym? (rozmawiam)
Miejscownik (Locative): o kim? o czym? (mówię)
Wołacz (Vocative): o!
There is no difference in sentence structure in Polish for this. The listener ascertains the meaning of the speaker from the context of the conversation. For example, in English, you wouldn't say "Right now, I don't wear socks." You'd say "Right now, I'm not wearing socks." In Polish the "right now" is the context that determines your meaning.
"nosić" (to wear) takes Accusative, but when a verb that took Accusative gets negated, it takes Genitive instead. This is the only case which changes when negated, other ones just stay the same.
However, one user recently pointed to me that the Clothing section suddenly uses Genitive which wasn't exactly introduced before, and there's a "Negations" skill afterwards - so this sentence probably shouldn't be here. Removed.