После совещания я захожу в кабинет начальницы и говорю, что отчёт готов.

Because после always takes the genitive.

• совещание = meeting
• после совещания = after the meeting

So this is just a normal case pattern you need to learn with the preposition:

• после урока = after class
• после работы = after work
• после совещания = after the meeting

Also, Russian has no articles, so совещания can mean the meeting or a meeting, depending on context.

This is a very common feature of Russian: the present tense can be used for narration.

It can sound like:

• a vivid storytelling present, sometimes called the historical present
• or a description of a usual sequence of actions

So:

• После совещания я захожу... и говорю...
  can mean something like
  After the meeting, I go into the boss’s office and say...

In natural English, you might translate it as past depending on context:

• After the meeting, I went into my boss’s office and said...

If you wanted a straightforward past-tense Russian version, you would normally say something like:

• После совещания я зашёл в кабинет начальницы и сказал, что отчёт готов.

Захожу comes from заходить / зайти and here means go in, step into, or sometimes drop in.

In this sentence, захожу в кабинет is a very natural way to say I go into the office.

Comparison:

• иду в кабинет = I am going to the office / heading to the office
• вхожу в кабинет = I enter the office
  
  • more neutral or slightly more formal/literary
• захожу в кабинет = I go into the office / step in
  
  • very natural in everyday Russian

So захожу works well because it describes the action of going into the office as part of a sequence.

Because Russian uses different cases after в depending on whether you mean movement or location.

• в кабинет = into the office → accusative
• в кабинете = in the office → prepositional

Here the speaker is moving into the office, so Russian uses the accusative:

• я захожу в кабинет = I go into the office

Compare:

• я сижу в кабинете = I am sitting in the office
• я работаю в кабинете = I work in the office

Russian often expresses possession with a noun in the genitive case.

So:

• кабинет начальницы literally = office of the female boss
• natural English = the boss’s office

The basic form is:

• начальница = female boss / female superior

Its genitive singular is:

• начальницы

So:

• кабинет начальницы = the female boss’s office

If the boss were male, you would get:

• кабинет начальника = the male boss’s office

Russian does not use an apostrophe like English boss’s. It usually uses the genitive instead.

Because the noun is начальница, which is the feminine form.

In the sentence you see начальницы, which is the genitive singular of начальница.

So the sentence specifically refers to a female boss.

Compare:

• начальник = male boss / boss in a general masculine form
• начальница = female boss

So:

• кабинет начальника = the male boss’s office
• кабинет начальницы = the female boss’s office

Что here means that and introduces a subordinate clause.

So:

• говорю, что отчёт готов = I say that the report is ready

This is standard indirect speech in Russian.

Compare:

• Я говорю, что всё нормально. = I say that everything is fine.
• Он сказал, что придёт позже. = He said that he would come later.

In English, that is often optional:

• I say the report is ready
• I say that the report is ready

In Russian, что is normally expressed in this kind of sentence.

If you wanted direct speech instead, you could say:

• ...и говорю: Отчёт готов.
  = ...and I say: The report is ready.

Because готов is the short form of the adjective готовый, and short forms are commonly used in Russian as the predicate meaning is ready.

So:

• отчёт готов = the report is ready

This is the normal way to say it.

Compare:

• готовый отчёт = a ready/prepared report

That long form готовый is usually used before a noun as an attribute:

• готовый отчёт лежит на столе = the completed report is lying on the table

But when you want to say the report is ready, Russian normally uses the short form:

• отчёт готов

Also remember that Russian usually omits есть in the present tense, so:

• отчёт готов literally feels like report ready
• but it means the report is ready

Because что отчёт готов is a subordinate clause, and Russian normally separates subordinate clauses with a comma.

So the structure is:

• я говорю = main clause
• что отчёт готов = subordinate clause

That is why you get:

• я говорю, что отчёт готов

This is a very regular rule in Russian punctuation.

Because the same subject can apply to both verbs.

In:

• я захожу в кабинет начальницы и говорю...

the subject я belongs to both:

• я захожу
• (я) говорю

Russian does not need to repeat it unless there is a reason to emphasize it or avoid confusion.

English works the same way:

• I go into the office and say...

You would not normally say:

• I go into the office and I say...

unless you wanted extra emphasis.

Yes. In many Russian texts, ё is often written as е, so you may see both:

• отчёт
• отчет

They represent the same word.

However, the pronunciation is with ё, and the stress is on that syllable:

• отчёт

For learners, it is helpful to remember the form with ё, because it makes the pronunciation clearer.

Yes. Russian word order is flexible, and the version in the sentence is just a very natural, neutral one.

• После совещания comes first to set the time frame
• then the speaker describes the sequence of actions

So this order feels like:

1. after the meeting
2. I go into the boss’s office
3. I say the report is ready

Other word orders are possible, but they may shift emphasis:

• Я после совещания захожу в кабинет начальницы...
  puts a bit more focus on I
• В кабинет начальницы я захожу после совещания...
  gives stronger emphasis to the destination

The original sentence is a good neutral narrative order.