Learn Finnish: Kaupunki oli eilen hiljainen. - The city was quiet yesterday.

Oli is the past tense ("was") for the third-person singular (he, she, it). It comes from the verb olla (to be). If you wanted to say the city is quiet today, you would use the present tense on: Kaupunki on tänään hiljainen.

How would I make this sentence negative to say the city was not quiet?

You would use the negative word ei and change the main verb into its past participle form. For the verb olla, the "was not" form is ei ollut. The negative sentence is: Kaupunki ei ollut eilen hiljainen.

Is there a strict rule for where to put time words like eilen (yesterday)?

Finnish word order is quite flexible. Putting eilen right after the verb is very natural and neutral, but you could also place it at the beginning of the sentence if you wanted to emphasize the time: Eilen kaupunki oli hiljainen (Yesterday, the city was quiet).

Why is the adjective hiljainen (quiet) in its basic dictionary form here?

In Finnish, adjectives must match the noun they describe. Because the subject kaupunki (city) is a single, countable noun in its basic form (the nominative case), the adjective hiljainen stays in its basic form to match it.