Когда поезд подошёл к платформе, мы быстро вошли в вагон.

Because Когда поезд подошёл к платформе is a subordinate time clause: When the train pulled up to the platform. In Russian, subordinate clauses are normally separated from the main clause by a comma.

So the structure is:

• Когда поезд подошёл к платформе = subordinate clause
• мы быстро вошли в вагон = main clause

Even if the order changes, the comma stays:

• Мы быстро вошли в вагон, когда поезд подошёл к платформе.

This is about aspect.

• подошёл = perfective, meaning the action was completed: the train came up / pulled up to the platform
• подходил = imperfective, focusing more on the process: the train was approaching

In this sentence, the train reaches the platform, and then we boarded. That sequence fits the perfective verb подошёл very well.

So Russian is emphasizing a completed event:

• first, the train arrived at the platform
• then, we got in

In basic meaning, подойти often means to come up to / approach, and with people it can involve walking. But in Russian it is also used more broadly for things that move toward and arrive at something, including vehicles.

So with a train:

• поезд подошёл к платформе = the train pulled up to the platform / came up to the platform

This is a normal and natural use.

Because the preposition к takes the dative case and usually means to / toward.

The noun changes like this:

• платформа = platform
• к платформе = to the platform

So поезд подошёл к платформе literally means the train approached to the platform.

There are two things happening here: number and aspect.

1. Number
   • мы = we
   • so the past tense verb must be plural
   • therefore: вошли

Compare:

• я вошёл / вошла = I entered
• он вошёл = he entered
• она вошла = she entered
• мы вошли = we entered

2. Aspect
   • вошли is perfective
   • it shows a completed action: we got into the carriage

If you said входили, that would be imperfective and would sound more like were entering / used to enter / entered repeatedly, which does not fit this one completed event as well.

Because Russian uses different cases after в depending on whether you mean:

• movement into something → accusative
• location inside something → prepositional

Here we have movement:

• вошли в вагон = entered into the carriage

So we use вагон (accusative singular, same form as nominative for this noun).

Compare:

• Мы вошли в вагон. = We entered the carriage.
• Мы были в вагоне. = We were in the carriage.

Because поезд means the whole train, while вагон means a carriage / railcar / train car.

In Russian, when talking about boarding, it is very common to say:

• войти в вагон = to get into the carriage
• сесть в поезд = to get on the train

So the sentence focuses on physically entering one of the train’s cars.

Russian word order is flexible, so быстро вошли is natural and neutral.

• мы быстро вошли в вагон = we quickly entered the carriage

You could also say:

• мы вошли в вагон быстро

But that often sounds a bit more marked, as if you are emphasizing quickly.

So in this sentence, быстро вошли is the most natural neutral order.

Russian has no articles like a or the.

So:

• поезд can mean a train or the train
• платформа can mean a platform or the platform
• вагон can mean a carriage or the carriage

The listener understands from context whether something is definite or indefinite.

In this sentence, context makes it clear that we mean a specific train and platform.

The whole sentence is in the past tense.

Russian past tense is usually formed from the verb stem plus endings that show gender/number:

• masculine singular: -л
• feminine singular: -ла
• neuter singular: -ло
• plural: -ли

Examples from the sentence:

• подошёл = masculine singular past
  because поезд is masculine singular
• вошли = plural past
  because мы is plural

So the verb agrees with the subject in the past tense.

Because the subject is поезд (train), which is singular masculine.

So the past tense verb must also be singular masculine:

• поезд подошёл

If the subject were plural, then you would use подошли:

• поезда подошли к платформе = The trains pulled up to the platform.

Yes. Russian allows both orders:

• Когда поезд подошёл к платформе, мы быстро вошли в вагон.
• Мы быстро вошли в вагон, когда поезд подошёл к платформе.

Both are grammatical.

The version with Когда... first is often slightly more natural when setting the scene first: When the train pulled up..., we...

Not always. Когда simply means when, and the tense depends on the situation.

Examples:

• Когда поезд подошёл к платформе... = past
• Когда поезд подойдёт к платформе... = future
• Когда поезд подходит к платформе... = present / habitual

In your sentence, the event happened in the past, so the verb is in the past tense.

Yes, depending on the nuance.

Some common options are:

• вошли в вагон = entered the carriage
• сели в поезд = got on the train
• зашли в вагон = went into the carriage

Why вошли works well here:

• it clearly describes crossing the boundary and going inside
• it matches the physical action of entering the carriage after the train arrived

So вошли в вагон is very natural in this context.