Der Stern ist fern.

Because Stern is a masculine noun in German.

• der = the for masculine singular nouns in the nominative case
• die = the for feminine singular nouns
• das = the for neuter singular nouns

So:

• der Stern = the star

This is something you usually have to learn together with the noun: not just Stern, but der Stern.

It is in the nominative case because it is the subject of the sentence.

In Der Stern ist fern:

• Der Stern = the subject
• ist = the verb
• fern = a description of the subject

A good rough pattern is:

• The star is far away
• Der Stern ist fern

The thing that is something is usually in the nominative.

Because German main clauses normally follow the verb-second rule.

In a basic statement, the finite verb goes in position 2:

• Der Stern | ist | fern

Here:

1. Der Stern = first position
2. ist = second position

That is standard German sentence order.

Ist is the 3rd person singular form of sein = to be.

The subject is der Stern, which is:

• 3rd person
• singular

So German uses:

• ich bin = I am
• du bist = you are
• er/sie/es ist = he/she/it is

Since Stern is singular, you need ist.

Fern is an adjective meaning something like far or distant.

In this sentence, it comes after the verb ist, so it is being used predicatively. That means it describes the subject but does not take adjective endings.

Compare:

• Der Stern ist fern. = The star is far/distant.
• ein ferner Stern = a distant star

Notice the difference:

• after ist: fern
• before a noun: ferner (with an ending)

Because adjectives in German only take endings when they come before a noun.

So:

• der ferne Stern = the distant star
• ein ferner Stern = a distant star

But after sein, werden, or bleiben, the adjective usually stays in its basic form:

• Der Stern ist fern.

This is very similar to English:

• the distant star
• the star is distant

Yes, but it can sound a little more literary, elevated, or concise than everyday speech in some contexts.

German speakers also often say:

• Der Stern ist weit weg. = The star is far away.

Both are understandable, but:

• fern = shorter, more formal/literary, sometimes more abstract
• weit weg = very common in everyday speech

In a simple learning sentence, Der Stern ist fern is perfectly fine.

A simple English-friendly guide:

• der ≈ dare
• Stern ≈ shtern / stern with a German st
• ist ≈ ist
• fern ≈ fehrn

A few useful pronunciation notes:

• At the start of a word, German st is usually pronounced sht.
  So Stern sounds more like Shtern.
• The r in words like der and fern is often not strongly rolled in standard German.
• e in fern is pronounced more like eh than the English fur sound.

Because all nouns are capitalized in German.

So:

• der Stern
• das Haus
• die Frau

Even in the middle of a sentence, nouns keep a capital letter. That is one of the easiest visual clues for spotting nouns in written German.

Yes. That would mean A star is far away or One star is far away, depending on context.

Compare:

• Der Stern ist fern. = The star is far away.
  
  • a specific star
• Ein Stern ist fern. = A star is far away.
  
  • a non-specific star

So the article changes the meaning slightly, just as in English.

Yes, there is a historical relationship.

German and English are related languages, so some words come from older common roots.

• Stern and star are related words.
• fern and far are also historically related.

That does not mean they always match perfectly in modern usage, but it can help you remember them:

• Stern → think star
• fern → think far

Yes. Like English distant, German fern can be used both literally and figuratively.

Literal:

• Das Dorf ist fern. = The village is far away.

Figurative or abstract:

• Die Gefahr ist noch fern. = The danger is still far off.
• Das liegt fern. = That is unlikely / far from the case, depending on context.

So in Der Stern ist fern, it most naturally means physical distance.