Если завтра утром экзамен, мне лучше лечь спать пораньше.

Russian often omits the verb to be in the present tense.

So завтра утром экзамен literally looks like tomorrow morning exam, but it means there is an exam tomorrow morning or the exam is tomorrow morning.

A fuller version would be:

• Если завтра утром будет экзамен...

But in everyday Russian, leaving out будет here is very natural, especially in informal speech.

Если means if and introduces a condition:

• Если завтра утром экзамен... = If there’s an exam tomorrow morning...

It sets up the reason for the second part:

• мне лучше лечь спать пораньше = I’d better go to bed earlier

So the whole sentence has the structure:

• If X, then Y

In Russian, a subordinate clause introduced by если is separated by a comma from the main clause.

So:

• Если завтра утром экзамен, мне лучше лечь спать пораньше.

This is standard punctuation, just like English often uses a comma after an opening if clause:

• If the exam is tomorrow morning, I’d better go to bed early.

Завтра утром is a very common time expression meaning tomorrow morning.

Here:

• завтра = tomorrow
• утром = in the morning

Russian often uses the instrumental form for times of day in this kind of expression:

• утром = in the morning
• днём = in the daytime / during the day
• вечером = in the evening
• ночью = at night

So завтра утром is the normal way to say tomorrow morning.

Утром is the instrumental singular of утро.

In Russian, parts of the day are often used in the instrumental to express when something happens:

• утром = in the morning
• вечером = in the evening

So in завтра утром экзамен, утром is not a direct object or anything like that. It is simply part of the time expression.

This is a very common Russian pattern.

• мне лучше + infinitive literally means something like it is better for me to...
• In natural English, that usually becomes I’d better... or it’s better for me to...

So:

• мне лучше лечь спать = I’d better go to bed

The pronoun is in the dative case because Russian treats this as a kind of impersonal expression:

• мне = to me / for me

Similar patterns:

• мне нужно идти = I need to go
• мне пора спать = it’s time for me to sleep

This is about verb aspect.

• лечь = perfective
• ложиться = imperfective

After лучше, Russian often uses the perfective infinitive when talking about a single complete action that should be done:

• мне лучше лечь спать = I’d better go to bed

This focuses on the one action of getting into bed.

If you used ложиться, it would sound more like a general habit or process, not this one specific action right now.

A useful contrast:

• Мне лучше лечь спать сейчас. = I’d better go to bed now.
• Мне лучше ложиться спать раньше. = I’d better start going to bed earlier.
  (more like a general habit)

Лечь спать is a fixed expression meaning to go to bed (to sleep).

Literally:

• лечь = to lie down
• спать = to sleep

Together, they mean to go lie down in order to sleep.

This is slightly different from just спать, which means to sleep.

Compare:

• Я хочу спать. = I want to sleep.
• Я хочу лечь спать. = I want to go to bed.

Пораньше means a bit earlier or fairly early, depending on context.

It comes from раньше = earlier.
The prefix по- often makes it softer or more practical in tone:

• раньше = earlier
• пораньше = a little earlier / nice and early

So:

• лечь спать пораньше = go to bed a bit earlier / go to bed early

In this sentence, natural English is usually just go to bed early.

Good question. Both relate to earliness, but they are not the same.

• рано = early
• раньше = earlier
• пораньше = a bit earlier / somewhat early

So:

• лечь спать рано = go to bed early
• лечь спать пораньше = go to bed a bit earlier than usual / go to bed nice and early

In this sentence, пораньше suggests comparison with the speaker’s normal bedtime, even if that comparison is only implied.

Yes.

Both are possible:

• Если завтра утром экзамен...
• Если завтра утром будет экзамен...

The version without будет is more compact and conversational.
The version with будет is fuller and more explicit.

Both mean essentially the same thing here.

Not completely. Russian word order is flexible, though different orders can shift emphasis.

The given sentence is very natural:

• Если завтра утром экзамен, мне лучше лечь спать пораньше.

You could also say:

• Если экзамен завтра утром, мне лучше лечь спать пораньше.

This puts a little more focus on экзамен first.

In the second part, мне лучше is the most natural order.
Something like лучше мне лечь спать пораньше is possible, but it sounds more marked and can shift emphasis.

Because it is the main noun in a clause meaning there is an exam or the exam is...

In завтра утром экзамен, Russian uses a verbless structure, and экзамен stays in the nominative:

• экзамен = nominative singular

You can think of it as the subject of an implied есть / будет type of idea:

• Завтра утром [есть / будет] экзамен.

Yes, depending on context.

• мне лучше лечь спать literally = it is better for me to go to bed
• In natural English, this often becomes:
  • I’d better go to bed
  • I should go to bed
  • It’s better if I go to bed

In this sentence, I’d better go to bed early is probably the best natural translation, because it conveys practical advice to oneself.

It is neutral and very natural in everyday speech.

The omission of будет in Если завтра утром экзамен makes it sound a little more conversational, but not sloppy or wrong. The whole sentence is perfectly normal in spoken Russian and also acceptable in writing unless the style needs to be especially formal.

Yes, but the meaning changes slightly.

• Мне лучше лечь спать пораньше = I’d better go to bed early
  (this sounds like good advice or the smart thing to do)

• Мне нужно лечь спать пораньше = I need to go to bed early
  (this sounds more necessary or required)

So лучше suggests recommendation, while нужно suggests necessity.