Ég kann ekki að sauma vel, svo hún sýnir mér hvernig ég á að halda á nálinni.

Here kann comes from kunna, which often means to know how to do something.

So Ég kann ekki að sauma vel is not mainly about physical possibility; it is about skill or learned ability:

• kunna = know how, be skilled at
• geta = can, be able to, manage to

A learner-friendly contrast:

• Ég kann að sauma. = I know how to sew.
• Ég get saumað núna. = I can sew now / I’m able to sew now.

In this sentence, sewing is treated as a skill, so kunna is the natural choice.

Because kunna að + infinitive is a common way to say know how to do something.

So:

• kunna að sauma = know how to sew
• kunna að syngja = know how to sing

Here að sauma is the infinitive phrase, and að introduces it.

In a normal Icelandic main clause, the negation ekki usually comes after the finite verb.

So:

• Ég kann ekki... = I do not know how / I can’t...
• not Ég ekki kann...

That word order is very standard in Icelandic.

Sauma means to sew, and vel means well.

So að sauma vel means to sew well.

The adverb vel modifies the verb sauma, just like well modifies to sew in English.

Here svo means so, therefore, or as a result.

It connects the two parts of the sentence:

• Ég kann ekki að sauma vel = I don’t know how to sew well
• svo hún sýnir mér... = so she shows me...

It is not the possessive svo from English-like patterns; it is a conjunction linking cause/result.

Because the verb sýna usually takes:

• the person shown something in the dative
• the thing shown as the direct object

So:

• hún sýnir mér = she shows me
• mér is the dative form of ég

A simple pattern is:

• að sýna einhverjum eitthvað = to show someone something

In this sentence, the thing being shown is not a single noun like the book; it is the whole clause:

• hvernig ég á að halda á nálinni

So mér is still dative because I am the person receiving the demonstration.

It is an embedded clause introduced by hvernig = how.

The whole clause means something like:

• how I should hold the needle
• how I am supposed to hold the needle

This entire clause functions as the object of sýnir:

• she shows me how I should hold the needle

So instead of showing a physical object, she is showing a method.

Yes, eiga often means to own / to have, but in the construction eiga að + infinitive, it means something like:

• should
• be supposed to
• be meant to

So:

• ég á að halda = I should hold / I am supposed to hold

This is a very common Icelandic structure and does not mean possession here.

Because eiga að + infinitive is the full construction.

So:

• á = finite form of eiga
• að halda = infinitive phrase

Together:

• ég á að halda = I should hold / I am supposed to hold

This að belongs to the eiga að construction, not to the earlier kunna að.

Because halda á is the idiomatic expression for hold something in the hand / be holding something.

So:

• halda á nálinni = hold the needle

Without the preposition, halda can have other meanings such as:

• keep
• maintain
• hold onto in a broader sense

For physical handling of an object, halda á is very common.

Nálinni is the dative singular definite form of nál (needle).

That happens because á in the expression halda á e-u governs the dative.

So:

• nál = needle
• nálinni = the needle, in dative singular

That is why you get:

• halda á nálinni = hold the needle

Because this is an embedded or subordinate clause, not a direct question.

Compare:

Direct question:

• Hvernig á ég að halda á nálinni?
• How should I hold the needle?

Embedded clause:

• hvernig ég á að halda á nálinni
• how I should hold the needle

In subordinate clauses, Icelandic normally keeps the subject before the finite verb:

• ég á not
• á ég

Yes, in natural English that is often the most idiomatic translation.

Literally, Ég kann ekki að sauma vel is closer to:

• I do not know how to sew well

But in everyday English, that often becomes:

• I can’t sew well

So the Icelandic emphasizes lack of skill, while English may express that with can’t.