Learn Turkish: Sonunda otobüs geldi. - Finally, the bus came.

It's the verb root gel (come) plus the direct past tense suffix -di. Because gel has an e as its vowel, vowel harmony rules dictate that the suffix takes an i, making it -di instead of -dı, -du, or -dü.

How would I make this negative, to say 'the bus didn't come'?

You add the negative suffix right after the verb root, before the past tense suffix. For gel-, vowel harmony gives us the negative suffix -me. When we add the past tense -di, we get gelmedi (did not come).

How does sonunda mean 'finally'? Are there suffixes attached to it?

Yes! The root word is son (end). We add -u (its), the buffer letter -n-, and the locative suffix -da (at/in/on). Literally, it translates to 'at its end', which is the Turkish way to say 'finally' or 'in the end'.

Why isn't there a suffix on otobüs? Doesn't it need an ending to show it's the subject?

No, in Turkish, the subject of the sentence (the one doing the action) stays in its plain, dictionary form (known as the nominative case). Since the bus is the thing that came, otobüs doesn't take any extra suffixes here.