Ég hjálpa honum að velja bindi sem passar við skyrtuna.

The dictionary form is the infinitive að hjálpa = to help. In the present tense, the 1st person singular is also hjálpa:

• ég hjálpa = I help
• þú hjálpar = you help
• hann/hún/það hjálpar = he/she/it helps

So in this sentence, Ég hjálpa means I help, even though hjálpa looks the same as the infinitive without að.

Because hjálpa takes a dative object in Icelandic.

• hann = he
• honum = him (dative)

So:

• Ég hjálpa honum = I help him

This is something English speakers have to get used to: some Icelandic verbs require objects in cases other than the accusative.

Here að velja is the infinitive phrase to choose.

The pattern is:

• hjálpa einhverjum að gera eitthvað
  = help someone do/to do something

So:

• Ég hjálpa honum að velja ...
  = I help him choose ...

In other words, að here is the infinitive marker, like to in English.

Because Icelandic does not have an indefinite article like English a/an.

So a bare noun can mean:

• bindi = a tie or just tie, depending on context

If Icelandic wants to say the tie, it usually adds the definite article to the end of the noun instead.

In this sentence, bindi is the direct object of velja and is therefore accusative.

However, bindi is a neuter noun, and for many neuter nouns the nominative and accusative singular look the same. So:

• nominative: bindi
• accusative: bindi

That is why there is no visible change here.

Sem is the relative word meaning that, which, or who depending on context.

Here it introduces a clause describing bindi:

• bindi sem passar við skyrtuna
  = a tie that matches the shirt

So sem passar við skyrtuna tells you which kind of tie is meant.

Passar is the 3rd person singular present form of passa.

It is singular because the subject of that relative clause is sem, referring back to bindi, which is singular:

• bindi sem passar ...
  = a tie that matches ...

If the noun were plural, the verb would also be plural.

Here passa við means to match, to go with, or to suit well with.

So:

• passar við skyrtuna
  = matches the shirt / goes with the shirt

This is not mainly about physical size. In this sentence it is about style or color matching.

There are two things going on:

1. skyrtuna includes the definite article, so it means the shirt
2. After við, the noun is in the accusative

The noun is skyrta = shirt.
Its definite accusative singular form is skyrtuna.

So:

• skyrta = shirt
• skyrtan = the shirt (nominative)
• skyrtuna = the shirt (accusative)

And here við takes the accusative, so skyrtuna is the correct form.

In Icelandic, the definite article is usually added as an ending, not written as a separate word like English the.

So:

• skyrta = shirt
• skyrtan / skyrtuna = the shirt, in different cases

This is very normal in Icelandic. Instead of a separate word before the noun, the noun itself changes form.

The sentence has a very normal Icelandic structure:

• Ég — subject
• hjálpa — finite verb
• honum — indirect object
• að velja bindi — infinitive phrase
• sem passar við skyrtuna — relative clause describing bindi

So the sentence is built roughly like this:

• I help him
• to choose a tie
• that matches the shirt

This is a straightforward pattern in Icelandic, and the relative clause comes right after the noun it describes.