Ég þarf að sækja um starfið á netinu.

Þarf að means need to or have to.

• þarf = need / have to
• að introduces the infinitive, like to in English
• sækja is the infinitive verb

So Ég þarf að sækja um... means I need to apply...

The full verb is þurfa = to need.
Here it appears as þarf, which is the 1st person singular present form: I need.

Because Icelandic normally uses að + infinitive after verbs like þurfa.

So:

• Ég þarf að fara = I need to go
• Ég þarf að vinna = I need to work
• Ég þarf að sækja um starfið = I need to apply for the job

In this kind of sentence, að works much like English to.

Sækja um is a fixed verb + preposition combination meaning to apply for.

• sækja on its own can mean things like seek, fetch, or attend, depending on context
• sækja um specifically means apply for

So you should learn it as one unit:

• sækja um starf = apply for a job
• sækja um leyfi = apply for a permit

This is similar to how English uses apply for, not just apply by itself.

Because starfið means the job, while starf means a job or just job more generally.

• starf = job
• starfið = the job

Icelandic usually adds the definite article to the end of the noun instead of using a separate word like the.

So:

• starf = job
• starfið = the job
• hús = house
• húsið = the house

That ending is the definite article attached to the noun.

The noun starf is a neuter noun, and in this sentence it is singular and definite, so it becomes starfið.

A learner does not need to memorize the whole grammar at once, but the important idea is:

• Icelandic often puts the at the end of the noun
• the ending changes depending on gender, number, and case

Here, starfið is the correct form for the job in this sentence.

Yes. The preposition um normally takes the accusative case, and sækja um uses that pattern.

So the thing you are applying for goes in the accusative:

• sækja um starf
• sækja um starfið

For this noun, the accusative singular definite form is starfið.

This is a useful thing to remember as a chunk:

• sækja um + accusative

Á netinu means online or on the internet.

Literally:

• á = on
• netinu = the net / the internet

So the phrase means something like on the net.

In natural English, though, you would usually translate the whole sentence as I need to apply for the job online.

Because after á in a location meaning like this, Icelandic uses the dative case.

Here, á means on in the sense of location, so:

• base noun: net
• definite form in this phrase: netinu

Compare the idea:

• á netinu = on the internet
• á borðinu = on the table

So netinu is not random; it is the form required by the grammar of the phrase.

Yes, pretty much. It is a very natural Icelandic way to say online.

You may also hear:

• á internetinu = on the internet
• sometimes even online, borrowed from English in informal usage

But á netinu is a very common and natural expression.

Yes. In many contexts, Ég þarf að... can be translated as either:

• I need to...
• I have to...

The exact English wording depends on context.

So this sentence could mean:

• I need to apply for the job online
• I have to apply for the job online

Both are reasonable translations.

The basic word order here is:

• Ég = subject
• þarf = finite verb
• að sækja um starfið = infinitive phrase
• á netinu = adverbial phrase

So literally:

• I need to apply for the job online

This is a very normal Icelandic sentence pattern: subject + verb + að + infinitive + other information

Then you would use starf instead of starfið:

• Ég þarf að sækja um starf á netinu.

That means I need to apply for a job online.

So the contrast is:

• starf = a job
• starfið = the job

A few parts may stand out to an English speaker:

• Ég: the é sounds roughly like ye at the start
• þ in þarf: like th in thin, not like th in this
• æ in sækja: similar to the i in my, though not exactly the same
• ð in starfið: often a soft voiced sound like th in this
• netinu: stress is on the first syllable, as in almost all Icelandic words

A rough learner-friendly pronunciation guide would be something like:

yeg tharv ath SIGH-kya um STAR-vith au NEH-ti-nu

That is only approximate, but it can help as a starting point.