Learn Hardcore Russian: Учитель подробно объясняет правило.

“explains” – The teacher explains the rule (general / repeated action).
“is explaining” – The teacher is explaining the rule (action happening now).

Russian doesn’t have a separate continuous form (is explaining); the imperfective present covers both simple and continuous meanings. Context tells you which is meant.

What case is правило in, and why does it look like the dictionary form?

Правило is in the accusative case, singular, neuter.

For most inanimate neuter nouns, the accusative singular form is identical to the nominative singular form.

Nominative (dictionary form): правило
Accusative: правило (same form)

So even though it looks like the base form, its function in the sentence is a direct object (the thing being explained).

How do I know that учитель is the subject and правило is the object? There are no articles like “the” or “a”.

You work it out from word endings and meaning, not from articles (Russian has no articles).

Учитель ends in -ь and is a masculine noun in the nominative case → typical subject form.
Объясняет is a 3rd person singular verb → its subject must be a singular noun; учитель fits.
Правило is in the accusative case (same form as nominative here) and comes after the verb → typical direct object position.

So the structure is:

Учитель (subject)
подробно объясняет (verb phrase)
правило (object)

What part of speech is подробно, and what does it literally mean?

Подробно is an adverb.

It comes from the adjective подробный (detailed) and means “in detail” or “in a detailed way”, roughly “thoroughly” in this context.

So:

объясняет правило – explains the rule
подробно объясняет правило – explains the rule in detail / thoroughly

Can I move подробно to another position, like in English?

Yes, Russian word order is relatively flexible, though it affects emphasis.

All of these are grammatically correct:

Учитель подробно объясняет правило. – Neutral; focus on the detailed explaining.
Учитель объясняет правило подробно. – Slight emphasis on how it’s explained (at the end).
Подробно объясняет правило учитель. – Stronger emphasis on подробно, and also a bit on учитель as the one who does it (more stylistic / literary or contrastive).

In everyday speech, the original Учитель подробно объясняет правило is the most common and neutral.

Why isn’t there a word like “to” before правило, as in “explains the rule to…”?

In this sentence, правило is what is being explained, not to whom it is explained, so it is a direct object in the accusative with no preposition:

объяснять что? – правило (what? – the rule)

If you add a person (to whom the rule is explained), they are usually in the dative case:

Учитель подробно объясняет правило ученикам. – The teacher explains the rule in detail to the students.

Here:

правило – accusative (what?)
ученикам – dative (to whom?)

What is the gender and plural of учитель?

Учитель is masculine, even though it ends in -ь (many masculine nouns do).

Forms:

Nominative singular: учитель – teacher
Nominative plural: учителя́ – teachers (stress moves: учителя́)

A common feminine form is:

учительница – female teacher
Plural: учительницы

What is the difference between учитель and преподаватель? Both seem to mean “teacher.”

Both mean “teacher,” but usage differs somewhat:

Учитель – usually a school teacher (especially in primary and secondary school).
Преподаватель – more formal; often used for college/university instructors or instructors in courses, training programs, etc.

In this sentence, Учитель подробно объясняет правило, the image is more like a school teacher in class.

How would I say this sentence in the past and future?

Present (given):

Учитель подробно объясняет правило. – The teacher (is) explaining / explains the rule in detail.

Past (imperfective, process / repeated):

Учитель подробно объяснял правило. – The teacher was explaining / used to explain the rule in detail.

Future (imperfective, process / repeated):

Учитель будет подробно объяснять правило. – The teacher will be explaining / will explain (habitually) the rule in detail.

Future (perfective, one complete act):

Учитель подробно объяснит правило. – The teacher will explain the rule in detail (once, focusing on completion).

Here объясняет / объяснял / будет объяснять are imperfective, while объяснит is perfective.

Why is it объясняет, not объясняетcя? What would the reflexive form mean?

Объясняет – active: someone explains something.

Объясняется is reflexive / passive-like and often means “is explained” or “turns out / is accounted for by”.

Compare:

Учитель объясняет правило. – The teacher explains the rule.
Правило объясняется так. – The rule is explained like this.
Это объясняется тем, что… – This is explained by the fact that… / This is due to the fact that…

In your sentence, we need an active subject (teacher) explaining something, so объясняет is correct.

Could I use детально instead of подробно?

Yes, детально is also an adverb meaning “in detail”.

Учитель детально объясняет правило. – very similar to Учитель подробно объясняет правило.

Nuance:

Подробно – very common, neutral “in detail.”
Детально – sometimes sounds a bit more formal or technical, but in many contexts they are close in meaning and interchangeable.

How is this sentence pronounced, and where are the stresses?

Stresses (marked with ´):

учи́тель – uchee-til
подро́бно – padrob-na
объясня́ет – ob-yas-nyá-et (the я is stressed; the initial объя- is pronounced smoothly, not as two totally separate syllables)
пра́вило – prá-vi-la

Altogether: учи́тель подро́бно объясня́ет пра́вило.