Mi ĵus venkis.

Because the ending -is marks the past tense in Esperanto.

So:

• venki = to win / to defeat
• venkas = wins / is winning
• venkis = won
• venkos = will win

In Mi ĵus venkis, the speaker is talking about something that happened a moment ago, so the past tense is used.

ĵus is an adverb meaning just, just now, or a moment ago.

It tells you that the action happened very recently. In this sentence, it modifies venkis, so the whole idea is I just won or I won just now.

Esperanto usually does not need a separate verb like English have to express this idea.

English often says:

• I have just won

Esperanto normally says:

• Mi ĵus venkis

The adverb ĵus already makes it clear that the action happened very recently, so the simple past tense is enough.

The base form is venki.

That is the infinitive, meaning to win or to defeat.

Esperanto verbs are very regular:

• venki = infinitive
• venkas = present
• venkis = past
• venkos = future
• venkus = conditional
• venku = command / jussive

It can mean either, depending on context.

• venki iun = to defeat someone
• venki en konkurso or simply venki = to win, be victorious

So Mi ĵus venkis can work as I just won, even without saying what was won. The context tells you what kind of victory it was.

Because Esperanto can leave the object unstated when it is obvious or unimportant.

English also does this:

• I won.

You do not always need to say:

• I won the game.
• I defeated my opponent.

Likewise, Mi ĵus venkis is a complete sentence by itself.

Yes, but Mi ĵus venkis is more natural.

Esperanto word order is fairly flexible, especially with adverbs. However, placing ĵus before the verb is the most straightforward way to show that it modifies the action:

• Mi ĵus venkis = the normal phrasing

Mi venkis ĵus is understandable, but it sounds less natural in ordinary usage.

ĵ is pronounced like the s in measure or the g in mirage.

So ĵus sounds approximately like zhoos:

• ĵ = zh
• u = oo
• s = s

The stress is on the only vowel: ĵus.

It is pronounced roughly VEN-kis.

A few pronunciation points:

• e is like the e in met
• i is like ee in see, but shorter
• stress in Esperanto is always on the second-to-last syllable

So ven-kis has the stress on ven.

No. Esperanto does not automatically capitalize the first-person pronoun.

English always writes I with a capital letter, but Esperanto uses mi in lowercase unless it begins a sentence:

• Mi ĵus venkis.
• Li vidis min.

So the capital M here is only because it is the first word of the sentence.

This is a very common question.

• venki = to defeat, to overcome, to be victorious
• gajni = to gain, to earn, to win something

Examples:

• Mi venkis mian kontraŭulon. = I defeated my opponent.
• Mi gajnis premion. = I won a prize.

In many contexts, English win can correspond to either verb, depending on what you mean. In Mi ĵus venkis, the focus is on being victorious rather than on receiving a prize or gaining something.