Det tager tid at skabe tillid, men kun et øjeblik at miste den.

Because Danish uses det as a dummy subject in expressions like det tager tid = it takes time.

Here, det does not refer to any specific thing. It works just like English it in it takes time.

Because both nouns are being used in a general, abstract sense:

• tid = time in general
• tillid = trust in general

So Danish says:

• det tager tid = it takes time
• skabe tillid = create/build trust

You would not normally use en/et here.

At is the infinitive marker, the equivalent of English to before a verb.

So:

• at skabe = to create
• at miste = to lose

There are two instances of at because the sentence contains two infinitive phrases:

• at skabe tillid
• at miste den

Yes. Skabe tillid is a very natural Danish expression and means create trust or build trust.

A very common alternative is opbygge tillid, which is even closer to English build trust.

So all of these are natural, though with slightly different shades:

• skabe tillid = create/build trust
• opbygge tillid = build up trust

Plain bygge tillid is understandable, but it sounds more influenced by English and is less idiomatic than opbygge tillid.

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

You simply have to learn the gender with the noun:

• et øjeblik = a moment

This is one of those things that is mostly lexical: the noun just happens to be an et-word.

Den refers back to tillid.

So:

• miste den = lose it
• and it = trust

Even though tillid appears without an article, it still has grammatical gender. Tillid is a common-gender noun, so the pronoun is den, not det.

Because the pronoun must match the gender of the noun it refers to.

• common gender noun → den
• neuter noun → det

Since tillid is common gender, Danish uses den.

Because Danish often leaves out repeated words when they are easy to understand from the context.

The full version would be:

Det tager tid at skabe tillid, men det tager kun et øjeblik at miste den.

In the original sentence, the second det tager is omitted because it would be repetitive. This kind of shortening is very natural.

Because kun et øjeblik belongs together as the time expression: only a moment.

In the full version:

det tager kun et øjeblik at miste den

the structure is:

• det tager = it takes
• kun et øjeblik = only a moment
• at miste den = to lose it

When det tager is omitted, the remaining part stays in the same basic order.

Yes, you could.

• miste den = lose it
• miste tilliden = lose the trust / lose trust

In this sentence, miste den sounds very natural because it avoids repeating tillid. Repeating the noun would still be grammatical, but slightly heavier stylistically.

Yes. A comma before men is standard in Danish.

So the punctuation in the sentence is completely normal:

Det tager tid at skabe tillid, men kun et øjeblik at miste den.