Learn Croatian: Vidio ju je jučer. - He saw her yesterday.

Croatian frequently drops subject pronouns like on (he) because the verb forms give enough clues. The helper verb je tells us it is a third-person subject (he, she, or it), and the -o ending on the main verb vidio tells us the subject is masculine. Together, they mean "he saw".

I thought the short word for "her" was je. Why is it ju here?

You are right that the short word for "her" (the direct object) is usually je. But notice the helper verb in this sentence is also je. To avoid saying je je (which sounds awkward), Croatian has a strict rule: whenever the helper verb is je, the word for "her" changes to ju.

Why is the word order Vidio ju je instead of putting the helper verb first (Vidio je ju)?

Both ju (her) and je (helper verb) are "clitics" — short, unstressed words that must clump together in a specific order. The rule in Croatian is that the helper verb je must always be the very last clitic in the chain.

How is the past tense formed in this sentence?