Learn Russian: Я не смог прийти вчера.

We use смог because it refers to failing to manage something on one specific, single occasion (вчера). If you used the imperfective мог, it would sound more like you generally lacked the ability or permission to come over a continuous period of time.

Why is the infinitive "прийти" also perfective?

After a modal verb like смог (managed to), we choose the infinitive's aspect based on what we are trying to do. The speaker failed to achieve the specific result of arriving. Since the focus is on a single completed result rather than the ongoing process of traveling, we need the perfective прийти.

How do we know the person speaking is a man?

The past tense verb смог is in the masculine form. Past tense verbs in Russian change based on gender. If a woman were speaking, she would add an -а to the end and say Я не смогла прийти вчера.

Why does "прийти" have a short "й" in it, when the basic verb for "to go" is "идти"?

This is a common spelling quirk with verbs of motion! When the prefix при- (which adds the meaning of arrival) attaches to the base verb идти, the spelling changes and the и becomes a short й in the infinitive.