En septembro komenciĝos la nova semestro, do mi denove aĉetos kajerojn kaj plumojn.

En means in, and en septembro is the normal way to say in September.

Esperanto often uses en + month/time word for this kind of time expression:

• en januaro = in January
• en somero = in summer

So En septembro is a very natural phrase.

The ending -os marks the future tense in Esperanto.

So:

• komenciĝos = will begin
• aĉetos = will buy

Esperanto does not need a separate word like will. The future meaning is built directly into the verb ending.

This is a very common question.

• komenci usually means to begin/start something and is often transitive, so it can take a direct object.
• komenciĝi means to begin, to start, with the idea that the subject itself comes into a new state.

So:

• Mi komencos la lecionon. = I will begin the lesson.
• La leciono komenciĝos. = The lesson will begin.

In your sentence, the semester is the thing that begins, so komenciĝos is the right form.

The element -iĝ- often shows that something becomes something or starts being in a certain state. It frequently turns a verb into an intransitive one.

So komenciĝi is roughly to begin / to get started.

It is not exactly the same as an English passive. It is more like a change or entering into a state.

Esperanto word order is fairly flexible. The subject does not always have to come before the verb.

So:

• La nova semestro komenciĝos en septembro.
• En septembro komenciĝos la nova semestro.

Both are correct.

In this sentence, putting En septembro first gives a little more emphasis to the time: In September, the new semester will begin.

La means the.

It is used here because the speaker is talking about a specific semester, not just any semester. In context, it is the upcoming new semester that both speaker and listener can identify.

So la nova semestro = the new semester.

• semestro is a noun, so it ends in -o
• nova is an adjective, so it ends in -a

In Esperanto, adjectives agree with the nouns they describe in number and case. Here both words are singular and not accusative, so we get:

• nova semestro

If it were plural, it would be:

• novaj semestroj

Do means so, therefore, or thus.

It connects the two parts of the sentence logically:

• the new semester will begin in September,
• so I will buy notebooks and pens again.

It is a very common word for showing a result or conclusion.

Denove means again.

It is an adverb, so it can move around somewhat, but placing it before the verb is very natural:

• mi denove aĉetos = I will buy again

You could also say:

• mi aĉetos denove

Both are possible, though the emphasis may shift slightly.

Because they are:

1. plural objects, and
2. direct objects of aĉetos

In Esperanto:

• -j = plural
• -n = accusative/direct object

So:

• kajeroj = notebooks
• kajerojn = notebooks as a direct object

And:

• plumoj = pens
• plumojn = pens as a direct object

Since the speaker is buying them, they are direct objects, so they need -n.

Yes. Each direct object noun normally takes its own correct ending.

So:

• kajerojn kaj plumojn is correct

Not:

• kajerojn kaj plumoj

Both nouns are plural direct objects, so both need -jn.

A few letters here are especially important:

• ĉ in aĉetos sounds like ch in church
• ĝ in komenciĝos sounds like j in judge
• c in komenciĝos sounds like ts in cats

So roughly:

• aĉetos ≈ ah-CHE-toss
• komenciĝos ≈ ko-men-TSI-joss

Also, Esperanto stress normally falls on the second-to-last syllable:

• sepTEMbro
• komeNCIĝos
• aĈEtos