Ŝia rolo komenciĝas per monologo.

Ŝi means she, while ŝia means her in the possessive sense.

• ŝi = she
• ŝia = her

In Ŝia rolo, the word ŝia describes rolo, so it works like an adjective: her role.

Like other Esperanto adjectives, possessive words such as mia, via, lia, ŝia, ĝia, nia, ilia usually end in -a.

Rolo means role, as in a part played by an actor, or more generally a function or position.

Examples:

• Ŝi havas gravan rolon en la teatraĵo. = She has an important role in the play.
• Lia rolo en la teamo estas klara. = His role in the team is clear.

It is a regular Esperanto noun:

• rolo = role
• roloj = roles
• rolon = role (direct object form)

Komenciĝas comes from:

• komenc- = begin/start
• -iĝ- = become, begin to be, undergo a change
• -as = present tense

So komenciĝas means begins in the sense of starts by itself / comes into a beginning state.

This is a very common Esperanto distinction:

• komenci ion = to begin something
• komenciĝi = to begin, to start

Examples:

• Ŝi komencas la paroladon. = She begins the speech.
• La parolado komenciĝas. = The speech begins.

In your sentence, the role is not beginning something else; the role itself begins, so komenciĝas is the natural form.

The suffix -iĝ- often shows that something becomes a certain way or undergoes a change of state. It often turns a more transitive idea into an intransitive one.

Examples:

• malfermi = to open something

• malfermiĝi = to open

• fermi = to close something

• fermiĝi = to close

• komenci = to begin something
• komenciĝi = to begin

So in komenciĝas, the idea is comes to its beginning or simply begins.

Here per means by means of, by way of, or more naturally in English here, with.

So komenciĝas per monologo means:

• begins with a monologue

A helpful way to think about per is that it introduces the means, method, or medium.

Examples:

• Mi skribas per krajono. = I write with a pencil.
• Li vojaĝas per trajno. = He travels by train.
• La programo komenciĝas per kanto. = The program begins with a song.

In English we often say with, but Esperanto commonly uses per in this type of structure.

Per and kun are different.

• per = by means of, by way of, using
• kun = with, together with, accompanied by

In this sentence, the monologue is the way the role starts, so per is the better choice.

Compare:

• La spektaklo komenciĝas per danco. = The show begins with a dance.
• Ŝi venis kun amiko. = She came with a friend.

So per monologo is about the form or means of beginning, not companionship.

Esperanto does not use la quite as automatically as English uses the.

Here, ŝia rolo is already definite enough because ŝia identifies whose role it is: her role. So la is usually unnecessary.

You could sometimes say la rolo de ŝi, but ŝia rolo is simpler and more natural.

Also, monologo appears without la because it means a monologue in a general sense. Esperanto has no separate word for a/an, so a bare noun can mean a monologue depending on context.

Because it is not a direct object.

The -n ending is used mainly for:

1. the direct object
2. motion toward something in some cases

Here, monologo comes after the preposition per, and prepositions normally do not take -n.

So:

• Ŝi verkas monologon. = She writes a monologue.
  
  • monologon is a direct object
• La rolo komenciĝas per monologo. = The role begins with a monologue.
  
  • monologo is the object of per, so no -n

Ŝia is pronounced roughly SHEE-ah.

Breakdown:

• ŝ sounds like English sh
• i sounds like ee
• a sounds like ah

So:

• ŝi = shee
• ŝia = shee-ah

The vowels are pronounced clearly and separately, not blended into one English-style sound.

Roughly: ko-men-TSEE-jahs

Breakdown:

• ko = koh
• men = men
• ci = tsoo/tsi sound, because c in Esperanto is always ts
• ĝ = like the j in jam
• as = ahss

More carefully:

• ko-men-ci-ĝ-as
• c = ts
• ĝ = j as in judge

So the word sounds approximately like ko-men-TSEE-jahs.

Yes, Esperanto word order is fairly flexible, but the normal order here is very natural:

• Ŝia rolo komenciĝas per monologo.

Because Esperanto marks grammar with endings and prepositions, you can sometimes move things around for emphasis. But for a learner, the standard order is best:

• possessor + noun
• subject
• verb
• prepositional phrase

So this sentence is a good model to follow.

You might see other ways to express a similar idea, but komenciĝas per monologo is the most straightforward and natural for learners.

Some related forms:

• komenciĝi = to begin
• ek- = indicates a sudden start or inception

For example:

• La pluvo ekis. = The rain started.

But with rolo in this sentence, komenciĝas is clearer and more idiomatic than trying to use ek- here.

So if your goal is natural standard Esperanto, Ŝia rolo komenciĝas per monologo is an excellent sentence.