Hun beklager sig over den lange kø ved bageriet.

Because at beklage sig is a fixed reflexive expression meaning to complain.

• at beklage by itself usually means to regret, to lament, or to apologize for / express sorrow about something.
• at beklage sig specifically means to complain.

So:

• Hun beklager sig = She complains
• Hun beklager det = She regrets it / She is sorry about it

The little word sig is essential here because it changes the meaning of the verb.

Sig is the reflexive pronoun, meaning something like herself / himself / itself / themselves depending on the subject.

In Danish, many verbs are reflexive, and sig is used with third-person subjects:

• Han vasker sig = He washes himself
• Hun beklager sig = She complains

With first and second person, Danish uses different reflexive forms:

• Jeg beklager mig = I complain
• Du beklager dig = You complain
• Hun beklager sig = She complains

So sig matches the subject hun.

Because at beklage sig over noget is the normal Danish pattern for to complain about something.

So:

• beklage sig over noget = complain about something

Examples:

• Han beklager sig over vejret = He complains about the weather
• Vi beklager os over støjen = We complain about the noise

This is just the preposition that belongs with this expression. English uses about, but Danish uses over.

This is because Danish uses a double definite structure when a noun has both:

1. a definite meaning, and
2. an adjective before the noun.

So instead of just attaching the definite ending to the noun, Danish normally uses:

• den/det/de + adjective + noun in indefinite form

Here:

• kø = queue/line
• den lange kø = the long queue

Why not den lang kø?
Because the adjective must take the correct form in this structure, and that form is lange.

Compare:

• en lang kø = a long queue
• den lange kø = the long queue

Because adjectives in Danish change form depending on grammar.

Here, lang becomes lange because it comes after den in a definite noun phrase:

• en lang kø = a long queue
• den lange kø = the long queue

This -e ending is very common in definite phrases.

You also see it in plural:

• lange køer = long queues

So in this sentence, lange is the correct definite form of the adjective.

Because kø is a common-gender noun in Danish.

Danish nouns are mainly either:

• common gender → takes en in the indefinite singular, and den in the definite phrase
• neuter gender → takes et in the indefinite singular, and det in the definite phrase

Since it is:

• en kø = a queue

it must be:

• den kø
• den lange kø

If the noun were neuter, you would use det instead.

Because bageriet is the definite form of bageri.

• et bageri = a bakery
• bageriet = the bakery

The ending -et is the normal definite ending for many neuter nouns.

So:

• ved bageri would sound incomplete or unnatural here
• ved bageriet = by/at the bakery

Ved usually means by, near, or at a place, while i means in/inside.

Here, ved bageriet suggests the queue is at the bakery, probably outside it or associated with it.

• ved bageriet = at/by the bakery
• i bageriet = inside the bakery

Since a queue is often outside or just at the location, ved is a natural choice.

Kø means queue, line, or waiting line.

For an English speaker, the pronunciation can be tricky because of ø. It is a vowel sound that does not exist exactly in English. It is pronounced with rounded lips, somewhat like a sound between English sir and French peu, depending on accent.

A few useful forms:

• en kø = a queue
• køen = the queue
• køer = queues
• i kø = in line

The spelling is short, but it is a very common everyday word in Danish.

Yes, absolutely. That is very natural Danish too.

• at klage over noget = to complain about something
• at beklage sig over noget = to complain about something

Both work, but there can be a slight difference in feel:

• klage over is often the most direct, common way to say complain about
• beklage sig over can sound a bit more like grumble or express dissatisfaction

In many everyday contexts, they are very close in meaning.

The sentence follows normal Danish main-clause word order:

• Hun = subject
• beklager sig = verb + reflexive pronoun
• over den lange kø ved bageriet = prepositional phrase

So the structure is:

Subject + verb + other elements

Danish main clauses usually put the finite verb in the second position:

• Hun beklager sig over den lange kø ved bageriet.

If you move something else to the front, the verb still stays in second position:

• Over den lange kø ved bageriet beklager hun sig.

That version is more marked, but grammatically it shows the same verb-second rule.

Not very naturally. A word-for-word translation would be misleading.

• sig does not need to be translated separately in normal English here
• over corresponds to English about, not literally over
• ved bageriet is best translated as at the bakery or by the bakery, depending on context

So even though the Danish parts are clear grammatically, the natural English translation has to be idiomatic rather than word-for-word. That is very common with reflexive verbs and prepositions.