Klokken kvart i otte finder jeg et ledigt sæde i metroen på den samme linje.

Kvart i otte means quarter to eight, so the time is 7:45.

In Danish time expressions:

• kvart over syv = quarter past seven
• halv otte = half to eight = 7:30
  (this is often tricky for English speakers)
• kvart i otte = quarter to eight

The word i here is part of the fixed time expression and corresponds to English to, not the usual meaning in.

This is a time expression placed first for emphasis or scene-setting: At quarter to eight...

In Danish, klokken + time is a normal way to say at [time]:

• Jeg kommer klokken otte = I’m coming at eight
• Klokken kvart i otte finder jeg... = At quarter to eight, I find...

Unlike English, Danish does not need a separate word like at before the time.

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

Here, the first element is the time phrase:

• Klokken kvart i otte = position 1
• finder = position 2
• jeg comes after the verb

So:

• Klokken kvart i otte finder jeg et ledigt sæde...

If the sentence started with jeg, then you would get:

• Jeg finder et ledigt sæde i metroen klokken kvart i otte.

Both are grammatical, but the first version emphasizes the time.

Yes. Finder is the present tense of at finde = to find.

• jeg finder = I find / I am finding

In Danish, the present tense is often used in narration or to describe what is happening in a sequence of events, so it can sound very natural even where English might choose a slightly different tense depending on context.

Because sæde is a neuter noun in Danish.

That affects both the article and the adjective:

• et sæde = a seat
• ledig = free / vacant / available
• with a neuter singular indefinite noun, the adjective gets -t
• so: et ledigt sæde

Compare:

• en ledig stol = a free chair
• et ledigt sæde = a free seat

Here ledig means free, vacant, or available.

So et ledigt sæde is a seat that is not occupied.

This word is also used in other contexts:

• en ledig stilling = a vacant job position
• Han er ledig = He is unemployed / out of work
  (depending on context)

So the core idea is that something is available or not currently taken.

Because metroen means the metro.

In Danish, definiteness is usually added to the end of the noun:

• en metro = a metro
• metroen = the metro

This is different from English, which normally uses a separate word (the).

So:

• i metroen = in the metro

These are two different prepositional ideas:

• i metroen = in the metro, meaning inside the train / in the metro system
• på den samme linje = on the same line, referring to the route or line

So Danish uses:

• i for being in the vehicle or system
• på for being on a line, route, platform, etc.

This is quite similar to English, where you might say:

• in the metro
• on the same line

Because linje is a common-gender noun, and Danish usually uses den samme before a singular definite common-gender noun.

So:

• en linje = a line
• den samme linje = the same line

A useful pattern is:

• den samme bog = the same book
• det samme hus = the same house

Here:

• den matches a common-gender noun
• samme does not change form here
• linje remains in its basic form after den samme

Yes. In many contexts, kvart i otte by itself is perfectly natural.

For example:

• Vi ses kvart i otte. = See you at quarter to eight.
• Jeg kommer klokken kvart i otte. = I’m coming at quarter to eight.

Including klokken can make the time expression feel a bit more explicit, but both are common and natural.

Yes. For example:

• Jeg finder et ledigt sæde i metroen på den samme linje klokken kvart i otte.

That is also grammatical, but it gives less emphasis to the time.

The original version starts with the time phrase to set the scene first:

• Klokken kvart i otte finder jeg...

So the choice is mainly about focus and style, not a change in basic meaning.