Afgangstavlen viser flynummeret.

In Danish, the definite article is usually attached to the end of the noun instead of written as a separate word.

• tavle = board
• tavlen = the board

and

• flynummer = flight number
• flynummeret = the flight number

So Danish often says the equivalent of board-the shows flight-number-the.

That is because the two nouns have different grammatical genders.

• en tavle → common gender → definite singular tavlen
• et nummer → neuter gender → definite singular nummeret

So:

• afgangstavlen = the departure board
• flynummeret = the flight number

A native English speaker often has to get used to the fact that Danish nouns have grammatical gender, and that this affects the definite ending.

Because the base noun is tavle, and when a common-gender noun ends in -e, the definite form is often just -n added to the word:

• en tavle → tavlen
• en pige → pigen

So you do not say tavleen.

Viser is the present tense of the verb at vise, meaning to show.

• at vise = to show
• viser = shows / is showing

In this sentence, Afgangstavlen viser flynummeret, it means The departure board shows the flight number.

Danish usually uses the simple present where English might use either the simple present or the present progressive.

So viser can mean:

• shows
• is showing

The exact meaning depends on context. In a sentence like this, Danish does not normally need a special progressive form.

It is a compound noun:

• afgang = departure
• tavle = board

Together:

• afgangstavle = departure board
• afgangstavlen = the departure board

Danish uses compound nouns very often, much like English does in words such as airport, bathroom, or flight number.

It is also a compound noun:

• fly = airplane / flight-related
• nummer = number

Together:

• flynummer = flight number
• flynummeret = the flight number

This is very typical Danish: instead of using several separate words, Danish often combines them into one noun.

No, this is a very normal Danish word order: subject + verb + object.

• Afgangstavlen = subject
• viser = verb
• flynummeret = object

So it works very much like English:

• The departure board
  • shows
    • the flight number

They are definite because the sentence is referring to specific things:

• the departure board
• the flight number

If you wanted a more general or indefinite meaning, the sentence would look different:

• En afgangstavle viser et flynummer.
• A departure board shows a flight number.

So the definite endings help show that the speaker has a particular board and a particular flight number in mind.

The indefinite singular forms are:

• en afgangstavle = a departure board
• et flynummer = a flight number

The sentence uses the definite forms instead:

• afgangstavlen = the departure board
• flynummeret = the flight number

Learning both the indefinite form and the definite form together is very useful in Danish.

No. Danish nouns are not normally capitalized the way German nouns are.

In this sentence, Afgangstavlen starts with a capital letter only because it is the first word of the sentence. If it appeared in the middle of a sentence, it would normally be written afgangstavlen.

A rough English-style approximation would be:

AF-gangs-tav-len VEE-ser FLY-num-mer-ed

A few notes:

• afgangstavlen is said as one word
• viser has a soft Danish s sound at the end
• fly has a vowel sound that does not exist exactly in English, so it may take practice
• nummeret often sounds more like num-mer-ed than a very clear num-mer-et

A more Danish-like pronunciation will come with listening practice, but it is good to start by treating the compound nouns as single units.