Ef við hefðum tekið betra kort, hefðum við ekki villst á stígnum.

They are past perfect subjunctive forms.

This sentence describes an unreal past situation: something that did not happen, and its imagined result.

• hefðum tekið = would have taken / had taken
• hefðum villst = would have gotten lost / had gotten lost

In Icelandic, counterfactual if-sentences like this commonly use the subjunctive in both parts.

Because each clause has its own verb phrase.

The sentence has two clauses:

1. Ef við hefðum tekið betra kort
   = if we had taken a better map

2. hefðum við ekki villst á stígnum
   = we would not have gotten lost on the path

Each clause needs its own auxiliary verb, so hefðum appears in both.

This is because of Icelandic verb-second word order in main clauses.

The whole if-clause comes first:

• Ef við hefðum tekið betra kort

That first clause counts as occupying the first position in the sentence, so in the main clause the finite verb must come next:

• hefðum við ekki villst á stígnum

If the main clause stood alone, you would normally say:

• Við hefðum ekki villst á stígnum.

So both are correct, but after the opening if-clause, Icelandic moves the finite verb to second position.

Villst is the past participle of villast, which means to get lost or to lose one’s way.

So:

• að villast = to get lost
• við hefðum villst = we would have gotten lost / we would have lost our way

This is a very common Icelandic verb when talking about navigation, direction, and losing the way.

Because kort is a neuter singular noun, and the adjective must agree with it.

Here betri is the basic comparative form better, but when it is declined to match kort, it becomes:

• masculine: betri
• feminine: betri
• neuter: betra

So:

• betra kort = a better map

Here kort is the direct object of tekið, so it is in the accusative.

The verb taka usually takes an accusative object:

• taka kort = take a map

Because kort is a neuter noun, its nominative and accusative singular forms look the same, so you do not see a change in the noun itself.

The adjective still shows the agreement clearly:

• betra kort

Because the sentence means a better map, not the better map.

Icelandic often expresses definiteness with a suffixed article on the noun. Since this is indefinite, there is no definite article attached.

So:

• betra kort = a better map
• betra kortið = the better map

Stígnum is dative singular definite of stígur = path, trail.

Breakdown:

• stígur = a path / trail
• stígnum = the path / the trail, in the dative

The ending -num includes the definite article, so stígnum means the path or the trail.

The preposition á can take different cases:

• accusative for motion toward/onto something
• dative for location or being on something

Here á stígnum means on the path / on the trail, so the dative is used.

Because in compound verb forms, ekki usually comes after the finite auxiliary and before the non-finite part.

So:

• hefðum við ekki villst

Structure:

• hefðum = finite auxiliary
• ekki = not
• villst = past participle

This is very normal Icelandic word order.

Yes. This is a very standard pattern for if ... would have ... sentences about the past.

Pattern:

• Ef + subject + subjunctive past perfect,
• subjunctive past perfect + subject + ...

So this sentence is a textbook example of:

• If we had taken a better map, we wouldn’t have gotten lost.

Yes, if it stands by itself, or if nothing else is taking the first position.

For example:

• Við hefðum ekki villst á stígnum.
  = We wouldn’t have gotten lost on the path.

But when the sentence begins with the if-clause, Icelandic main-clause word order changes:

• Ef við hefðum tekið betra kort, hefðum við ekki villst á stígnum.

So the difference is mainly about sentence structure, not meaning.

Ef means if.

It introduces the conditional clause:

• Ef við hefðum tekið betra kort
  = If we had taken a better map

In sentences like this, ef introduces the condition, and the other clause gives the imagined result.

Yes, kort can mean map, and it can also mean card in other contexts. The exact meaning depends on context.

In this sentence, because of took a better map and got lost on the path, kort clearly means map.

So context tells you which sense is intended.