Depois da palestra, a professora falou sobre o processo para conseguir estágio.

Because Portuguese normally contracts de + a into da.

• depois de = after
• a palestra = the lecture/talk
• depois da palestra = after the lecture/talk

This kind of contraction is very common in Portuguese:

• de + o = do
• de + a = da
• de + os = dos
• de + as = das

So depois da palestra is the natural form.

Palestra usually means a talk, lecture, or presentation, especially a somewhat formal one.

Depending on context, it could be:

• a lecture at school or university
• a professional talk
• a guest presentation
• a workshop-style talk

It is not usually the same as a normal class lesson. For a regular class, Portuguese would more often use aula.

Portuguese uses definite articles much more often than English does.

So where English says:

• the teacher spoke... or even just
• Teacher spoke... (in some contexts)

Portuguese very naturally says:

• a professora falou...

Here, a professora means the teacher/professor and refers to a specific female teacher already known in the situation.

This is very normal in Portuguese:

• o professor chegou
• a médica explicou
• o João saiu cedo

English often drops the article where Portuguese keeps it.

Because professora is the feminine form and professor is the masculine form.

• o professor = the male teacher/professor
• a professora = the female teacher/professor

Portuguese nouns referring to people often change form to match gender.

Falou is the preterite form of falar for ele/ela/você.

• falar = to speak / to talk
• ela falou = she spoke / she talked

The preterite is used for a completed action in the past. Here, it means the teacher spoke at that moment after the lecture.

Compare:

• ela falou = she spoke / she did speak
• ela falava = she used to speak / she was speaking / she would speak

So falou presents the event as finished.

Because Portuguese often omits subject pronouns when the subject is already clear.

In this sentence, a professora is already the subject, so there is no need to add ela.

• a professora falou = the teacher spoke

Adding ela would usually be unnecessary here.

This is very common in Portuguese:

• João chegou cedo
• minha irmã trabalha muito
• o diretor explicou tudo

The verb form and context usually make the subject clear enough.

Here sobre means about or regarding.

• falou sobre o processo = spoke about the process

With falar, sobre is very common when introducing a topic.

Examples:

• falar sobre política = talk about politics
• falar sobre o projeto = talk about the project

You may also see falar de, which can sometimes also mean talk about, but falar sobre often sounds a bit more explicit or formal when referring to a topic.

This phrase means something like the process for getting an internship.

It breaks down like this:

• o processo = the process
• para = for / in order to
• conseguir = to get / to obtain / to manage to get
• estágio = internship

So para conseguir estágio literally means to get an internship or in order to get an internship.

In natural English, the whole phrase may be translated more smoothly as:

• the process for getting an internship
• how to get an internship

Because after para, Portuguese often uses the infinitive to express purpose.

• para estudar = to study / in order to study
• para trabalhar = to work / in order to work
• para conseguir estágio = to get an internship / in order to get an internship

This works a lot like English to + verb or in order to + verb.

Conseguir often means to get, to obtain, or to manage to get/do.

In this sentence, it suggests successfully obtaining an internship, not just applying for one.

So:

• conseguir estágio = get an internship / secure an internship

Depending on context, Portuguese could also use verbs like:

• obter = obtain
• arranjar = get/find
• buscar = seek

But conseguir is very common and natural in everyday Brazilian Portuguese.

Portuguese often leaves out the article when speaking in a more general sense.

So:

• conseguir estágio = get an internship / secure internship experience in general

If you say:

• conseguir um estágio = get an internship

that is also correct and very natural. It can sound slightly more concrete: one internship.

If you say:

• conseguir o estágio

that would usually mean get the internship, referring to a specific one already known.

So the version without an article is general and idiomatic.

It could appear in some contexts, but falou sobre is the clearest and most standard choice for spoke about.

• falou sobre o processo = spoke about the process
• falou do processo = talked about the process

Both can be correct, but sobre is often preferred when introducing the topic directly and clearly.

Yes, it is natural and appropriate here.

Depois da palestra is an introductory time expression:

• After the lecture, ...

In Portuguese, as in English, a comma is commonly used after this kind of opening phrase, especially in careful writing.

Without the comma, the sentence would still be understandable, but the comma makes the structure clearer and more polished.

Yes. Portuguese allows some flexibility.

The original:

• Depois da palestra, a professora falou sobre o processo para conseguir estágio.

Other possible orders:

• A professora falou sobre o processo para conseguir estágio depois da palestra.

Both are correct. The version with Depois da palestra at the beginning puts more emphasis on the time setting first. That is very common in narration and written Portuguese.