Learn Polish: Wczoraj napisał długi list. - He wrote a long letter yesterday.

Because the action is completely finished. napisał is the perfective form of the verb. We use it when the focus is on the result of a completed action (the letter is written). If we used pisał, it would mean he was in the process of writing it, but maybe never finished.

Where is the word for 'he' in this sentence?

In Polish, you can usually leave out pronouns like on (he) because the verb itself tells us who did the action. The -ł at the end of napisał shows that it was a single male doing the action in the past tense.

Since długi list is the object of the verb, shouldn't its ending change?

It actually is in the accusative case (the case for direct objects), but because list is a masculine inanimate noun (a thing, not a living person or animal), its accusative form looks exactly the same as its basic dictionary form. The adjective długi just copies this behavior.

Why does the adjective długi end in -i and not the usual masculine -y?

Normally, basic masculine adjectives end in -y (like dobry). However, Polish spelling rules say you cannot write y after the letters k or g. Because of the g in this word, it has to take an -i ending instead.