Learn Hardcore Japanese: asita no asa ni sakana wo kaimasu.

あした (ashita): the most common everyday word for “tomorrow.”
あす (asu): a bit more formal or literary.
みょうにち (myōnichi): very formal or used in fixed expressions (e.g. official schedules).
In this sentence, you’d use あした.

Why is there a の between 明日 and 朝?

Here の functions like a genitive/possessive marker, linking two nouns.
明日の朝 literally means “tomorrow’s morning,” i.e. “tomorrow morning.”

Why do we use に after 朝? Can it be omitted?

に marks a specific point in time when something happens.

朝に = “in/at the morning”
In casual speech, you can drop に for many time phrases (e.g. 明日の朝魚を買う), but including に is more precise and common in polite or written Japanese.

Why is を used after 魚?

を marks the direct object of a verb. You’re buying 魚 (“fish”), so 魚を買います = “(I) buy fish.”

Why is the verb 買います at the end of the sentence?

Japanese normally follows a Subject–Object–Verb (SOV) word order. Verbs (and adjectives) always come at the end of their clause.

Can I reorder the sentence, for example 魚を明日の朝に買います?

Yes. Japanese word order is flexible, but putting the time expression first is the most natural:
明日の朝に魚を買います.

What’s the difference between 買います and 買う?

買います is the polite –masu form (used in formal or polite contexts).
買う is the plain/dictionary form (used in casual speech).
To sound more casual, you could say 明日の朝に魚を買う.