Wir steigen am Bahnhof in den Zug ein.

Because einsteigen is a separable verb.

The full verb is einsteigen = to get in / to board. In a normal present-tense main clause, the verb splits:

• Wir steigen ... ein.

So:

• steigen goes to the usual verb position
• ein moves to the end

Compare:

• Wir steigen ein. = We get in / board.
• Wir wollen in den Zug einsteigen. = We want to board the train.

In the second example, einsteigen stays together because it is at the end in the infinitive.

Here, einsteigen means to get into / board a vehicle.

It is very commonly used for:

• den Zug = the train
• den Bus = the bus
• das Auto = the car

So Wir steigen in den Zug ein means We are getting onto / into the train or We are boarding the train.

It does not usually mean climbing in a general physical sense. It is especially common for entering transport.

Because einsteigen tells you the action, but in den Zug tells you what you are getting into.

• Wir steigen ein. = We are getting in / boarding.
  (But into what? That is not stated.)
• Wir steigen in den Zug ein. = We are getting into the train.

So the phrase after it gives the destination of the movement.

Because in can take either the accusative or the dative, depending on meaning.

Here there is movement into something, so German uses the accusative:

• in den Zug = into the train

If it were about being inside the train already, German would use the dative:

• im Zug = in the train

So compare:

• Wir steigen in den Zug ein. = We get into the train.
• Wir sitzen im Zug. = We are sitting in the train.

This is a very important German pattern:

• location → dative
• direction/movement toward a new place → accusative

Am Bahnhof is short for an dem Bahnhof.

• an + dem = am

Here it means at the station.

German uses an with certain places in an idiomatic way, and am Bahnhof is the normal expression for at the train station.

So:

• am Bahnhof = at the station
• im Bahnhof = in the station building

That is an important difference:

• am Bahnhof usually focuses on the station as a location/stop
• im Bahnhof focuses more on being physically inside the building

In am Bahnhof, Bahnhof is in the dative.

Why? Because:

1. am = an dem
2. dem is the dative article for masculine and neuter nouns
3. Bahnhof is masculine: der Bahnhof

Also, the phrase describes a location:

• We are boarding at the station

That is not movement toward the station in this sentence. It is the place where the action happens.

The sentence follows the normal German main-clause pattern:

• Wir = subject
• steigen = finite verb in second position
• am Bahnhof = place
• in den Zug = direction/object of the action
• ein = separated prefix at the end

So:

• Wir steigen am Bahnhof in den Zug ein.

German often keeps the finite verb in position 2, and with a separable verb the prefix goes to the end.

Yes. German word order is flexible, as long as the verb rules are respected.

For example, you could also say:

• Am Bahnhof steigen wir in den Zug ein.

That puts more emphasis on am Bahnhof.

You may also hear:

• Wir steigen in den Zug am Bahnhof ein.

This is possible, but it can sound less natural depending on context, because am Bahnhof is usually understood as the setting of the whole action and often comes earlier.

The most important rule is that in a main clause:

• the conjugated verb stays in position 2
• the separable prefix stays at the end

Not exactly.

• einsteigen = to get in / board a vehicle
• besteigen = to board / climb onto

For everyday speech about trains, buses, and cars, einsteigen is much more common and natural.

Examples:

• Wir steigen in den Zug ein. = normal everyday German
• Wir besteigen den Zug. = grammatically possible, but much less common in ordinary conversation

So for a learner, einsteigen is usually the better choice here.

Because a train is something you go inside, not onto.

German usually uses:

• in for enclosed vehicles: in den Zug, in den Bus, ins Auto
• auf for things you sit/stand on: auf das Fahrrad, auf das Pferd

So:

• in den Zug einsteigen = get into / board the train
• auf das Fahrrad steigen = get onto the bicycle

Yes.

If the context is clear, German often leaves it out:

• Wir steigen jetzt ein. = We’re getting in / boarding now.

If everyone already knows you are talking about the train, there is no need to repeat in den Zug.

The main dictionary forms are:

• wir = we
• einsteigen = to get in / board
• der Bahnhof = train station
• der Zug = train
• in = in / into
• an = at / on / by

Useful article information:

• der Bahnhof → dem Bahnhof in dative
• der Zug → den Zug in accusative

When einsteigen appears in an infinitive or a subordinate clause, it stays together.

Examples:

• Wir möchten am Bahnhof in den Zug einsteigen.
  Here einsteigen is an infinitive, so it stays together.

• ..., weil wir am Bahnhof in den Zug einsteigen.
  In a subordinate clause, the full verb goes to the end.

So the splitting happens mainly in normal main clauses with a conjugated separable verb:

• Wir steigen ... ein.