Hællinn brotnaði í gær, svo ég fór með skóna til skósmiðs í morgun.

The ending -inn is the suffixed definite article, so:

• hæll = heel
• hællinn = the heel

Here hællinn is the subject of the sentence, so it is in the nominative singular.

brotna means to break, become broken in an intransitive sense. It describes something ending up broken without focusing on who did it.

So:

• Hællinn brotnaði = the heel broke / got broken

This is different from brjóta, which is transitive and means to break something.

• Ég braut hælinn = I broke the heel

So brotnaði is the natural choice when the heel is the thing that broke.

These are fixed time expressions:

• í gær = yesterday
• í morgun = this morning / in the morning

In Icelandic, time expressions often use prepositions in ways that do not match English exactly, so it is best to learn these as whole phrases.

A very useful contrast is:

• í morgun = this morning
• á morgun = tomorrow

Those two are easy to confuse at first.

Here svo connects the two clauses and means something like so, therefore, or and then.

It shows the result or next step:

• the heel broke yesterday,
• so I took the shoes to the shoemaker this morning.

fór is the past tense of fara, which usually means to go.

But fara með e-ð is a common expression meaning to take/bring something along or to take something somewhere.

So:

• ég fór með skóna = I took the shoes / I went with the shoes

In this sentence, the natural English meaning is that the speaker took the shoes to the shoemaker.

skóna is the accusative plural definite form of skór.

Very roughly:

• skór = shoe
• skóna = the shoes

It appears here because it is the object of fór með. In context, the shoes usually means the pair of shoes, not just several random shoes.

The preposition til takes the genitive case.

The dictionary form is skósmiður = shoemaker / cobbler.
Its genitive singular is skósmiðs.

So:

• til skósmiðs = to a shoemaker / to the shoemaker

This is a very common pattern in Icelandic: after til, expect a genitive form.

Icelandic does not have a separate word for a/an, and it often uses a bare noun where English would choose a or the from context.

So til skósmiðs can mean:

• to a shoemaker
• to the shoemaker

depending on the situation.

If you wanted to make it explicitly definite, you could say til skósmiðsins.

Yes, that can also be possible, but the structure is a little different.

In svo ég fór..., svo works as a conjunction, and the clause keeps normal main-clause order:

• ég fór

In svo fór ég..., svo is more like an adverb placed first in the clause, which causes inversion:

• fór ég

Both patterns exist, but svo ég fór... is a very straightforward way to connect the two ideas.

Yes. It is a compound noun:

• skó- from skór = shoe
• smiður = smith, craftsman

So it literally means something like shoe-smith, which is why it means shoemaker or cobbler. Compound nouns are extremely common in Icelandic.