Sjálfsafgreiðslan virkar, svo ég leita í bókasafnskerfinu.

Because Icelandic usually puts the definite article on the end of the noun instead of using a separate word like English the.

• sjálfsafgreiðsla = self-service / self-checkout
• sjálfsafgreiðslan = the self-service / the self-checkout

This noun is feminine, and in the nominative singular the definite form becomes -an here.

So the sentence is referring to a specific self-checkout system, not just self-checkout in general.

It is a compound noun.

• sjálfs- = self-
• afgreiðsla = service, checkout, handling

So sjálfsafgreiðsla literally means something like self-service or self-checkout.

Icelandic makes very heavy use of compounds, so long words like this are normal.

virkar is the present tense, 3rd person singular, of virka, which means to work, to function, or to operate.

So:

• ég virka = I work/function
• þú virkar = you work/function
• hann/hún/það virkar = he/she/it works/functions

Here the subject is sjálfsafgreiðslan, which is singular, so virkar is the correct form.

Usually just works, but Icelandic present tense often covers both ideas depending on context.

So Sjálfsafgreiðslan virkar can mean:

• The self-checkout works
• The self-checkout is working

Icelandic does not use a progressive tense like English as often, so the simple present often does more work.

Here svo means so or therefore.

It links the two clauses:

• Sjálfsafgreiðslan virkar = The self-checkout works
• svo ég leita í bókasafnskerfinu = so I search in the library system

Be aware that svo can also mean then, thus, or like that in other contexts. Its exact meaning depends on how it is used.

Because here svo is functioning as a conjunction meaning so.

After a conjunction like this, Icelandic normally keeps regular main-clause word order:

• svo ég leita...

If svo were being used more like an adverb meaning then, you could more naturally get inversion:

• Svo leita ég... = Then I search...

So the word order helps show how svo is being understood.

Because leita is the correct 1st person singular present indicative form here.

Present tense of leita:

• ég leita = I search
• þú leitar = you search
• hann/hún/það leitar = he/she/it searches
• við leitum = we search
• þið leitið = you (plural) search
• þeir/þær/þau leita = they search

leiti is a different form, used in the subjunctive, not the ordinary present statement used here.

Because leita í means search in something, like searching in a database, a book, a catalog, or a system.

That is different from leita að, which means look for something.

Compare:

• Ég leita í bókasafnskerfinu. = I search in the library system.
• Ég leita að bókinni. = I am looking for the book.

This is an important distinction:

• leita í + dative = search in
• leita að + dative = look for

Because the preposition í is required after leita in this meaning, and í takes the dative case when it means location or being inside something.

So:

• bókasafnskerfi = library system
• í bókasafnskerfi would be incomplete here and also missing the definite form
• í bókasafnskerfinu = in the library system

The ending -inu shows:

• neuter singular
• definite
• dative

So bókasafnskerfinu means the library system in the dative case.

It is another compound noun.

At its core:

• kerfi = system
• bókasafn = library

Together:

• bókasafnskerfi = library system

Then the definite dative singular form is:

• bókasafnskerfinu = in the library system

You can also see how Icelandic stacks compounds:

• bók = book
• bókasafn = library, literally something like book collection
• bókasafnskerfi = library system

This kind of long compound-building is extremely common in Icelandic.

Because the speaker is talking about specific, known things:

• sjálfsafgreiðslan = the self-checkout
• bókasafnskerfinu = the library system

In English, we use a separate word the. In Icelandic, that definiteness is often attached to the noun itself.

Using the definite form makes the sentence sound like it refers to particular systems available in the situation, not just any self-checkout or any library system.

It is understandable and grammatical. The main thing to notice is the pattern leita í for searching in a system or database.

Depending on context, Icelandic speakers might also use other verbs such as:

• fletta upp í = look up in
• leita að = look for
• skoða = check, inspect, browse

But leita í bókasafnskerfinu is a very natural way to say search in the library system.