Если на кухне появится дым, лучше сразу выключить плиту и открыть окно.

Because this sentence talks about a possible future event: if smoke appears in the kitchen.

In Russian, after если (if), you can use a future form when the meaning is truly future. That is different from English, where we usually say If smoke appears..., not If smoke will appear...

• появится = future, perfective, it will appear
• появляется = present, imperfective, it appears / is appearing / appears regularly

Here, the speaker means a single possible event in the future, so появится is the natural choice.

Russian often uses the perfective aspect for single completed events.

появиться means to appear / to show up, viewed as one complete event. In this sentence, the smoke is not being described as a process in progress; the idea is that it comes up / appears. So perfective fits well.

Compare:

• Если появится дым... = If smoke appears...
• Если появляется дым... = If smoke appears / keeps appearing... in a more general or repeated sense

So the perfective here makes the condition sound like a specific incident.

Russian usually says на кухне for in the kitchen when talking about being in that room.

This is just the standard idiomatic choice in Russian. Some locations use в, some use на, and learners often just have to memorize the common pattern.

• на кухне = in the kitchen
• в комнате = in the room
• в ванной = in the bathroom

So even though English uses in, Russian prefers на кухне.

Кухне is in the prepositional case.

That is because it follows на in a location meaning:

• на кухне = in the kitchen / on the kitchen premises

The base noun is:

• кухня = kitchen

In the prepositional singular:

• кухня → кухне

So на кухне literally means on/in the kitchen in Russian usage.

Because дым is the subject of появится.

It is the thing that appears:

• дым появится = smoke will appear

Subjects in Russian are normally in the nominative case, so дым stays nominative here.

Here лучше means something like:

• it is better to...
• you’d better...
• it’s best to...

It is being used impersonally to give advice or a recommendation.

So:

• лучше сразу выключить плиту и открыть окно
  = it’s better to turn off the stove right away and open the window

This is a very common Russian pattern:

• Лучше подождать. = It’s better to wait.
• Лучше не спорить. = Better not argue.

Because they depend on лучше.

After лучше, Russian often uses the infinitive to express what action is advisable:

• лучше сделать = it is better to do
• лучше уйти = it is better to leave

So here:

• лучше сразу выключить плиту и открыть окно

means:

• it’s better to immediately turn off the stove and open the window

Russian does not need an explicit you should here.

They are perfective because the sentence recommends single completed actions:

• выключить плиту = turn off the stove
• открыть окно = open the window

The focus is on getting those actions done, not on the process.

If you used imperfective forms, the meaning would change or sound less natural here:

• выключать = to be turning off / to turn off habitually
• открывать = to be opening / to open repeatedly

For an urgent instruction about one situation, perfective is the normal choice.

Both are direct objects of the infinitives, so they are in the accusative case.

• выключить что? → плиту
• открыть что? → окно

Forms:

• плита → плиту (accusative singular)
• окно → окно (neuter nouns like this often have the same form in nominative and accusative singular)

So:

• выключить плиту = turn off the stove
• открыть окно = open the window

Сразу means immediately / right away / at once.

Here it modifies the recommended actions:

• лучше сразу выключить плиту и открыть окно

It suggests quick action.

Its placement is natural because it comes before the infinitive phrase it affects. Russian word order is flexible, but this position sounds very normal.

You could also hear slightly different word orders depending on emphasis, but this one is standard and clear.

Because Russian often leaves out a generic subject when giving advice, instructions, or general statements.

English often says:

• you should turn off the stove
• you’d better open the window

Russian can simply say:

• лучше выключить плиту и открыть окно

The person understood as the one who should act is implied from context. This is very common.

Yes, but the meaning would change slightly.

• лучше = it’s better / you’d better
  This gives advice or a recommendation.
• надо / нужно = it is necessary / one must / need to
  This sounds more like necessity.

Compare:

• Если на кухне появится дым, лучше сразу выключить плиту и открыть окно.
  = If smoke appears in the kitchen, it’s better to immediately turn off the stove and open the window.

• Если на кухне появится дым, надо сразу выключить плиту и открыть окно.
  = If smoke appears in the kitchen, you need to immediately turn off the stove and open the window.

So лучше is a bit softer and more like practical advice.

No, Russian word order is fairly flexible, but the given order is very natural.

The sentence is structured as:

• Если
  • condition
• then the advice in the main clause

So:

• Если на кухне появится дым, лучше сразу выключить плиту и открыть окно.

This is a normal, neutral way to say it.

You could rearrange parts for emphasis, but the basic meaning would remain the same. For learners, the given version is a very good model to follow.