Learn Polish: Mamy zielony stół. - We have a green table.

In Polish, the verb ending already tells you who is doing the action. The -my ending in mamy means "we have." You can add the pronoun my for emphasis, but it is usually left out in everyday speech.

The verb mieć (to have) requires the accusative case. Why do zielony and stół look like they are in the basic dictionary form?

They actually are in the accusative case here! For masculine inanimate nouns like stół (objects that aren't alive), the accusative form looks exactly the same as the basic nominative form. The adjective zielony simply copies this rule to match the noun.

How would this sentence change if I wanted to say "We DO NOT have a green table"?

It would become Nie mamy zielonego stołu. This is an important rule in Polish: when you negate a sentence with a direct object, the noun and its adjective must change from the accusative case to the genitive case.

Why does the word stół use the letter ó instead of a regular u?

The letter ó is pronounced exactly like the Polish u (like the "oo" in the English word "boot"). It is used here because historically it was an "o" sound, and it still changes back to a regular o in other grammatical forms of the word, such as the genitive form stołu.