Learn Hardcore Latin: Plebs in foro clamat. - The common people shout in the forum.

Because plebs is grammatically singular in Latin. It is a collective noun: it refers to a crowd or body of people, but Latin treats it as one unit.

So:

plebs = nominative singular
clamat = he/she/it shouts or is shouting, 3rd person singular

That is why the verb is singular, not plural.

What case is plebs, and how do we know it is the subject?

Plebs is in the nominative singular, which is the case normally used for the subject of a sentence.

We know it is the subject because:

it is in the nominative case
the verb clamat is singular and agrees with it
in foro is a prepositional phrase, so it is not the subject

So the basic structure is:

plebs = subject
clamat = verb
in foro = where the action happens

Why is foro in the ablative?