La unua raŭndo komenciĝas nun.

Unu means one as a number.
Unua means first as an ordinal.

So:

• unu raŭndo = one round
• la unua raŭndo = the first round

Esperanto usually forms ordinals by adding -a to the number word:

• du → dua = second
• tri → tria = third

La is the definite article, meaning the.

So la unua raŭndo means the first round, not just a first round or first round in a general sense.

Unlike English, Esperanto has only one article:

• la = the

There is no separate word for a/an.

Because it is built from several meaningful pieces:

• komenc- = begin, start
• -iĝ- = become, get into a state
• -as = present tense

So komenciĝas literally has the idea of is becoming started or more naturally is starting / begins.

This is a very common Esperanto pattern: a root plus endings that show how the action works.

This is a very common learner question.

• komencas = starts/begins something
• komenciĝas = starts/begins by itself, begins

Examples:

• Mi komencas la ludon. = I start the game.
  Here, someone is actively starting something.
• La ludo komenciĝas. = The game starts / is beginning.
  Here, the game itself is beginning.

In your sentence, la unua raŭndo is the thing that begins, so komenciĝas is the natural choice.

-iĝ- is an Esperanto suffix that often means become, get, or come to be.

It often turns something into an intransitive idea, where the subject undergoes a change rather than acting on something else.

Examples:

• ruĝa = red

• ruĝiĝi = to become red

• fermi = to close something
• fermiĝi = to close, become closed

So:

• komenci = to start something
• komenciĝi = to begin, to get started

In Esperanto, -as marks the present tense.

So komenciĝas means begins / is beginning.

The basic tense endings are:

• -as = present
• -is = past
• -os = future
• -us = conditional
• -u = command or wish
• -i = infinitive

So you could compare:

• komenciĝas = begins
• komenciĝis = began
• komenciĝos = will begin

Yes, raŭndo is a normal Esperanto noun meaning round. It is a borrowing, adapted to Esperanto spelling and sound patterns.

Pronunciation:

• raŭn-do
• The stress falls on the second-to-last syllable: RAŬNdo

About aŭ:

• aŭ is a diphthong, roughly like ow in English cow, though exact pronunciation may vary.

The letter ŭ is very short and is used mainly in combinations like:

• aŭ
• eŭ

Because -o is the standard noun ending in Esperanto.

So:

• raŭndo = round
• unua = first, adjective
• nun = now, adverb

A very important pattern in Esperanto is:

• -o = noun
• -a = adjective
• -e = adverb

That makes it easier to see each word’s role in the sentence.

Because unua is an adjective, and adjectives in Esperanto end in -a.

It describes the noun raŭndo, so it must be an adjective:

• unua raŭndo = first round

Also, adjectives agree with the nouns they describe in number and case.
Here everything is singular and there is no accusative, so plain -a is enough.

The -n ending usually marks the direct object, and there is no direct object here.

In La unua raŭndo komenciĝas nun, the subject is la unua raŭndo. It is the thing that is beginning.

Since nothing is being directly acted upon, no accusative -n is needed.

You would see -n in a sentence like:

• Mi komencas la unuan raŭndon nun.
  = I am starting the first round now.

Here, la unuan raŭndon is the direct object, so it takes -n.

Yes, it can go somewhere else. Esperanto word order is fairly flexible, as long as the sentence stays clear.

All of these are possible:

• La unua raŭndo komenciĝas nun.
• Nun la unua raŭndo komenciĝas.
• La unua raŭndo nun komenciĝas.

Placing nun at the end is very natural and gives it a slight final emphasis, similar to now in English.

The subject is la unua raŭndo.

A good way to see that is to ask: What begins now?
Answer: the first round.

The verb is komenciĝas, and nun is just an adverb telling you when.

So the sentence breaks down like this:

• La unua raŭndo = subject
• komenciĝas = verb
• nun = time adverb

You might see eki in Esperanto, and it often means to start doing something suddenly or to begin.

So ekas can sometimes work in context, but komenciĝas is more straightforward and neutral here.

Compare:

• La unua raŭndo komenciĝas nun. = The first round begins now.
• La unua raŭndo ekas nun. = The first round starts now.

The first version is usually the safer and more standard choice for a learner.

In Esperanto, the stress is almost always on the second-to-last syllable.

So here:

• la = just la
• unua = u-NU-a
• raŭndo = RAŬN-do
• komenciĝas = ko-men-CI-ĝas
• nun = just nun

This regular stress rule is one of the nicest things about Esperanto pronunciation.