Nach der Landung gehen wir zur Gepäckausgabe.

Because nach takes the dative case when it means after in a time expression.

• die Landung = the landing (nominative)
• der Landung = the landing (dative)

So:

• nach der Landung = after the landing

This is a very common pattern:

• nach dem Essen = after the meal / after eating
• nach der Arbeit = after work
• nach dem Film = after the movie

Here, nach means after in a temporal sense.

So nach der Landung means after the landing.

Be careful: nach can also mean other things in other contexts, such as:

• to / toward with cities or countries without an article
  
  • nach Berlin = to Berlin
• according to
  
  • nach dem Plan = according to the plan

In this sentence, it clearly means after.

Because the sentence uses the verb gehen with a destination, and German often expresses that destination with a prepositional phrase.

• zu = to
• der Gepäckausgabe = the baggage claim / baggage reclaim area (dative)

So:

• zu der Gepäckausgabe = to the baggage claim area
• zur Gepäckausgabe = contracted form of zu der

The contraction is standard and very common:

• zu dem → zum
• zu der → zur

Because zu takes the dative case, and Gepäckausgabe is a feminine noun.

• die Gepäckausgabe = nominative
• der Gepäckausgabe = dative

So:

• zu der Gepäckausgabe → zur Gepäckausgabe

This is the same pattern as:

• zu der Schule → zur Schule
• zu der Tür → zur Tür

Landung is feminine: die Landung.

A useful clue is the ending -ung, which is almost always feminine in German.

Examples:

• die Landung = landing
• die Zeitung = newspaper
• die Rechnung = bill / invoice
• die Übung = exercise

So when you see a noun ending in -ung, you can usually assume it is feminine.

It is also feminine: die Gepäckausgabe.

The head word here is Ausgabe, which is feminine, so the whole compound noun is feminine.

German compound nouns take the gender of the last element:

• das Gepäck = luggage
• die Ausgabe = issue / distribution / dispensing
• die Gepäckausgabe = baggage claim / luggage pick-up area

This is a very important rule for compound nouns.

German main clauses usually follow the V2 rule: the finite verb comes in the second position.

Here, the first position is taken by the time phrase:

• Nach der Landung = position 1
• gehen = position 2
• wir = then comes the subject

So the structure is:

• Nach der Landung | gehen | wir | zur Gepäckausgabe

If you start with the subject instead, that is also possible:

• Wir gehen nach der Landung zur Gepäckausgabe.

Both are correct. The version with Nach der Landung first puts more emphasis on the time.

Yes, absolutely.

That version is also natural and correct. The difference is mainly one of focus:

• Nach der Landung gehen wir zur Gepäckausgabe.
  Emphasizes when this happens.
• Wir gehen nach der Landung zur Gepäckausgabe.
  Starts more neutrally with we.

German is flexible about what comes first, but the finite verb still stays in second position in a main clause.

The main verb is simply gehen = to go.

The destination is added with the preposition zu:

• gehen
  • zu
    • dative

So:

• zur Gepäckausgabe gehen = to go to the baggage claim area

This is similar to English go to, except in German the zu is a separate preposition, not part of the verb itself.

Usually zur Gepäckausgabe is the most natural choice here.

Why?

• zu often means movement to a place / destination
• in emphasizes going into an enclosed space

At an airport, zur Gepäckausgabe is the standard way to say to baggage claim.

You might use in die ... if you really want to stress entering a room or area physically, but in everyday airport language zur Gepäckausgabe sounds more idiomatic.

Yes, in this context it means the place where you collect your checked luggage after a flight.

Depending on region and context, English might say:

• baggage claim
• baggage reclaim
• luggage claim
• luggage reclaim

In German, Gepäckausgabe is a standard and useful word for that airport area.

A simple pronunciation guide is:

Nahkh dare LAN-doong GAY-en veer tsoor geh-PEK-ows-gah-buh

A few notes:

• ch in nach is the rough sound heard in Scottish loch
• w in German sounds like English v
• z in zur sounds like ts
• gehen has a long e sound: GAY-en
• Gepäck is stressed on the second syllable: ge-PÄCK
• Ausgabe is stressed on the first syllable: AUS-gabe

There are two important prepositional phrases here:

1. nach der Landung

   • nach takes the dative
   • der Landung is dative feminine

2. zur Gepäckausgabe

   • zu takes the dative
   • zur = zu der
   • der Gepäckausgabe is dative feminine

So both nouns after the prepositions are in the dative case.

The subject wir is in the nominative, and gehen is the finite verb.