Когда я вхожу в библиотеку, я говорю «Здравствуйте».

Here когда introduces a time clause: when.

In this sentence, because both verbs are in the present tense, the meaning is usually habitual:

• Когда я вхожу в библиотеку, я говорю Здравствуйте.
• Whenever/when I enter the library, I say Hello.

So in English, when or whenever can both fit, depending on context.

This is a question of aspect.

• входить = imperfective
• войти = perfective

вхожу is the 1st person singular present of входить. The imperfective is used here because the sentence describes a repeated, usual action.

So:

• Когда я вхожу в библиотеку... = when/whenever I enter the library
• Когда я войду в библиотеку... = when I enter the library (one specific future time)

Also, войти does not have a true present-tense meaning. Forms like я войду are usually future.

Because Russian distinguishes between:

• motion toward/into a place
• location in a place

With в:

• в + accusative = into, to
• в + prepositional = in, inside

So:

• в библиотеку = into the library
• в библиотеке = in the library

Since вхожу means I enter / go into, Russian uses в библиотеку.

Because it is in the accusative singular.

библиотека is a feminine noun ending in -а, and many such nouns change like this:

• nominative: библиотека
• accusative: библиотеку

That happens because the preposition в here expresses motion into a place, which requires the accusative.

Yes, Russian often can omit personal pronouns when the verb already shows the subject clearly.

So these are both possible:

• Когда я вхожу в библиотеку, я говорю Здравствуйте.
• Когда вхожу в библиотеку, говорю Здравствуйте.

The version with я repeated sounds clear, balanced, and completely natural, especially for learners and in neutral written style.

Russian often keeps the pronoun when:

• the speaker wants clarity,
• there is contrast,
• or the sentence has two clauses and repeating the subject makes the structure easier to follow.

Because Когда я вхожу в библиотеку is a subordinate clause, and Russian normally separates subordinate clauses from the main clause with a comma.

So:

• Когда я вхожу в библиотеку, я говорю Здравствуйте.

This comma is required in standard Russian punctuation.

In Russian, говорить is very commonly used to introduce what someone says directly.

So я говорю Здравствуйте literally means:

• I say Hello
• or more naturally, I say “Hello”

This is normal Russian. You could also hear other verbs in different contexts, but говорю is simple and standard here.

Здравствуйте is a polite/formal greeting.

You use it:

• with strangers,
• with teachers,
• with staff,
• in official or polite situations,
• or when greeting more than one person.

It corresponds to English Hello, but with a stronger sense of politeness.

Compare:

• Здравствуй = informal, singular
• Здравствуйте = polite singular or plural

So in a place like a library, Здравствуйте is very appropriate.

Yes, it looks harder than it sounds.

A helpful stress-marked version is:

• Здрáвствуйте

Learners often pronounce every letter, but in real speech some sounds get reduced or simplified. A practical learner approximation is something like:

• ZDRA-stvooy-tye
  or
• ZDRA-stvooy-te

The important part is the stress on the first syllable: ЗДРА-.

You do not need perfect reduction right away; native speakers will still understand you if you pronounce it carefully.

It can mean either, depending on context.

вхожу is a present-tense imperfective form, so it may describe:

• an action happening now: I am entering
• a repeated/habitual action: I enter / I usually enter

In this sentence, the presence of когда and the overall structure strongly suggest the habitual meaning:

• When/whenever I enter the library, I say Hello.

So although вхожу can sometimes mean I’m entering, here it is best understood as a general routine.

A helpful stressed version is:

Когда́ я вхожу́ в библиоте́ку, я говорю́ Здра́вствуйте.

Word by word:

• когда́
• вхожу́
• библиоте́ку
• говорю́
• здра́вствуйте

Stress matters in Russian, so it is good to learn words together with their stress from the beginning.