Ved indgangen spørger jeg: “Undskyld, kan De vise mig garderoben, og får man et programblad der?”

Because Danish normally follows the V2 rule in main clauses: the finite verb comes in the second position.

• Jeg spørger ved indgangen = neutral word order, starting with I
• Ved indgangen spørger jeg = starting with At the entrance, so the verb spørger must come next

So when Ved indgangen is moved to the front, jeg has to come after the verb.

Ved indgangen means at the entrance or by the entrance.

• ved = at / by / near
• indgangen = the entrance

So it refers to the location where the speaker is asking the question.

Because indgangen is the definite form, meaning the entrance.

In Danish, the definite article is often attached to the end of the noun:

• en indgang = an entrance
• indgangen = the entrance

This is very common in Danish.

De is the formal/polite word for you.

It is capitalized to show respect and to distinguish it from de, which usually means they.

So:

• De = formal you
• de = they

This formal De is correct, but in modern spoken Danish it can sound quite formal or old-fashioned. In everyday speech, many Danes would simply say du instead.

Not very common in everyday conversation. It is much more formal than modern English you.

You may still see or hear it:

• in very polite service situations
• in older texts
• when someone wants to sound especially respectful

But most modern Danes would usually use du, even with strangers.

A more everyday version would be:

Undskyld, kan du vise mig garderoben ...

Because mig is the object form of jeg.

Compare:

• jeg = I
• mig = me

After a verb like vise (show), Danish uses the object form:

• kan De vise mig garderoben? = can you show me the cloakroom?

Just like in English, you say show me, not show I.

Garderoben means the cloakroom or the coat check.

Again, Danish puts the definite article at the end:

• en garderobe = a cloakroom / wardrobe
• garderoben = the cloakroom

In this sentence it refers to a specific cloakroom at the venue, so the definite form is natural.

Here man means one, you, or people in general.

It is very common in Danish when asking about what is generally possible or available:

• Får man kaffe her? = Do you get coffee here? / Is coffee available here?
• Kan man parkere der? = Can you park there?

So får man et programblad der? means something like:

• Do you get a program leaflet there?
• Can you get a program leaflet there?
• Is a program leaflet available there?

It sounds more general than asking about me personally.

Because yes/no questions in Danish usually begin with the finite verb.

So:

• statement: Man får et programblad der. = You get a program leaflet there.
• question: Får man et programblad der? = Do you get a program leaflet there?

This verb-first pattern is very common in Danish questions.

Yes, more or less.

• får = gets / receives
• man = one / you / people
• et programblad = a programme leaflet / program booklet
• der = there

In natural English, we would usually not translate it word for word. More natural translations are:

• Do you get a program leaflet there?
• Can you get a program leaflet there?
• Is there a program leaflet available there?

Yes, absolutely. In fact, many learners will hear this version often.

• Får man et programblad der? asks whether people are given one there
• Kan man få et programblad der? asks whether it is possible to get one there

In many real situations, the difference is small. The version with kan man få can sound a little more directly about availability.

Here der means there.

So:

• der = there

It points to a place, in this case probably the cloakroom or that area near it.

Do not confuse it with other uses of der, such as in relative clauses. Here it is simply a place word.

You may also sometimes see dér with an accent when the speaker wants to stress it especially, but the normal spelling is just der.

Because programblad is a neuter noun in Danish, so it takes et.

• et programblad = a program leaflet

A useful extra point: programblad is a compound noun:

• program
  • blad

In Danish compounds, the gender usually comes from the last part, and blad is a neuter noun, so the whole compound takes et.

Yes, it is understandable and correct, but it sounds somewhat formal, mainly because of De.

A modern everyday version might be:

Undskyld, kan du vise mig garderoben, og kan man få et programblad dér?

or even:

Undskyld, hvor er garderoben, og kan man få et programblad dér?

So the original sentence is fine, especially for practicing grammar and polite forms, but it is more formal than what many Danes would normally say in casual speech.