Það var hrein heppni að hún fann símann sinn undir sætinu.

Here það works like English dummy it in It was pure luck... It does not refer to a specific object.

So the pattern is:

Það var + noun phrase + að-clause

In this sentence:

Það var hrein heppni að ...
= It was pure luck that ...

If Icelandic used þetta instead, it would mean something more like this, which is not the idea here.

Because heppni is the complement of var and is in the nominative case here. The adjective has to match it.

• heppni = feminine singular nominative
• hrein = feminine singular nominative form of hreinn

So:

hrein heppni = pure luck

If the noun were in the accusative, you would expect hreina instead.

This phrase is also idiomatic: hrein heppni is a very natural way to say pure luck.

Here að means that and introduces a subordinate clause:

að hún fann símann sinn undir sætinu
= that she found her phone under the seat

So the whole structure is:

Það var hrein heppni að ...
= It was pure luck that ...

This is different from the other common að that marks an infinitive, as in að fara = to go.

Because after að, Icelandic normally uses subordinate-clause word order, with the subject before the verb:

að hún fann ...

This is similar to English:

that she found ...

In main clauses, Icelandic often has verb-second word order, but subordinate clauses introduced by að usually do not.

Fann is the past tense of finna, which means to find.

A few useful forms are:

• finna = to find
• finnur = finds / is finding
• fann = found
• fundið = found

It is an irregular verb, so the vowel changes and the past form has to be memorized.

Because símann is the direct object of fann, so it appears in the accusative case.

From the noun sími:

• síminn = the phone in the nominative
• símann = the phone in the accusative

So:

hún fann símann ...
= she found the phone ...

This is one of the most common things English speakers need to get used to in Icelandic: the noun changes form depending on its role in the sentence.

That is the normal Icelandic pattern with possessives very often, especially when the noun is definite.

So Icelandic commonly says:

• síminn minn = my phone
• símann sinn = her own phone

This can feel backwards to an English speaker, but it is standard Icelandic word order.

Also, the possessive changes form to agree with the noun in gender, number, and case.

Because sinn is the reflexive possessive. It refers back to the subject of its own clause, which here is hún.

So:

hún fann símann sinn
= she found her own phone

If you said:

hún fann símann hennar

that would usually mean:

she found her phone, where the phone belongs to some other woman, not to the subject hún herself.

This is a very important Icelandic distinction that English does not usually make.

Also, sinn appears in the form sinn here because it agrees with símann, which is masculine singular accusative.

Because undir can take either the accusative or the dative, depending on meaning.

• accusative: movement toward a position
• dative: location in a position

Compare:

• Hún setti símann undir sætið. = She put the phone under the seat.
  Movement, so accusative.

• Síminn var undir sætinu. = The phone was under the seat.
  Location, so dative.

In your sentence, undir sætinu tells us where the phone was when she found it, so it is a location phrase and uses the dative.

Because Icelandic uses the definite form when the seat is understood as a specific one in the situation.

So:

undir sætinu
= under the seat

This sounds natural if the speaker has a particular seat in mind, for example a seat in a car, bus, or room.

Also notice that Icelandic usually adds the definite article to the end of the noun instead of writing a separate word:

• sæti = seat
• sætinu = the seat, in the dative singular

So both símann and sætinu show the very common Icelandic pattern of a suffixed definite article.