Learn Russian: Студенты всегда голодны.

Голодны is a short-form adjective. Russian frequently uses short forms to describe personal states or conditions, like being hungry, busy, or ready. When used this way, the short form acts as the main predicate (the action or state) of the sentence.

How does the ending on голодны work?

Short-form adjectives change to match the noun they describe, but only in gender and number. Because студенты is plural, we use the plural ending -ы. For a single male student, it would be голоден, and for a female student, голодна.

The lesson says short forms are for temporary states. Since they are "always" hungry, why not use the regular long form?

Even though they are всегда (always) hungry, hunger is still a temporary physical condition or feeling, rather than an inherent permanent trait like being tall. Russian prefers short forms for these types of personal states (hungry, busy, sick, glad) regardless of how often they happen.

Where is the word for "are" in this sentence?

Just like with regular adjectives and nouns, Russian omits the verb "to be" (is, am, are) in the present tense. The short-form adjective голодны directly handles the job of saying "are hungry" all by itself.