Á fimmtudag förum við inn um innganginn, út um útganginn og svo beint heim.

In Icelandic, days of the week are commonly used with á to mean on a particular day.

• á = on
• fimmtudag = Thursday in the form needed here

So Á fimmtudag means on Thursday.

Because á takes the accusative here.

The basic dictionary form is:

• fimmtudagur = Thursday (nominative)

But after á in this kind of time expression, it becomes:

• fimmtudag (accusative)

So this is a case change, not a different word.

This is because Icelandic usually follows a verb-second pattern in main clauses.

When the sentence starts with something other than the subject, such as a time phrase like Á fimmtudag, the finite verb usually comes next:

• Á fimmtudag förum við ...

If the subject came first, then you would say:

• Við förum ...

Both are possible structures, but once Á fimmtudag is placed first, förum normally comes before við.

Förum is the 1st person plural present tense of fara, which means to go.

Because the subject is við = we, the verb must match it:

• við förum = we go

This verb is a bit irregular, so it is worth memorizing:

• ég fer = I go
• þú ferð = you go
• hann/hún/það fer = he/she/it goes
• við förum = we go
• þið farið = you go
• þeir/þær/þau fara = they go

They are directional adverbs:

• inn = in, inward
• út = out, outward

They show movement, not location.

So:

• inn um innganginn = in through the entrance
• út um útganginn = out through the exit

A useful contrast is:

• inn / út = movement
• inni / úti = being inside / outside

Here there is movement, so inn and út are the correct forms.

Here um means something like through or by way of.

So:

• inn um innganginn = in through the entrance
• út um útganginn = out through the exit

This is a very natural Icelandic pattern: a direction word like inn or út, followed by um plus the place you pass through.

Also, um takes the accusative case, which helps explain the forms innganginn and útganginn.

That -inn is the definite article, meaning the.

In Icelandic, the is usually attached to the end of the noun rather than written as a separate word.

So:

• inngangur = entrance
• innganginn = the entrance
• útgangur = exit
• útganginn = the exit

In this sentence, they are also in the accusative singular, because of um.

Very roughly:

• inngangur → inngang → innganginn
• útgangur → útgang → útganginn

More or less, yes.

A very close breakdown is:

• inn = in
• um = through
• innganginn = the entrance

So it is basically in through the entrance.

The same goes for:

• út um útganginn = out through the exit

This parallel structure is very neat and natural in Icelandic.

Here svo means then or after that.

So the sentence gives a sequence:

1. Á fimmtudag
2. förum við inn um innganginn
3. út um útganginn
4. og svo beint heim

So svo links the final step: and then straight home.

Beint means straight or directly here.

So:

• beint heim = straight home / directly home

Grammatically, beint is the neuter singular form of the adjective beinn, but Icelandic often uses this kind of form adverbially.

So even though beinn is an adjective, beint here functions like an adverb: it describes how they go home.

Because heim works as an adverb meaning home or homeward after verbs of motion.

So Icelandic says:

• fara heim = go home

This is actually similar to English, which also says go home, not go to home.

So beint heim is perfectly natural and means straight home.

A fairly close word-for-word reading is:

On Thursday go we in through the entrance, out through the exit, and then straight home.

That is not natural English word order, but it helps show the Icelandic structure.

A natural English version would be:

On Thursday we go in through the entrance, out through the exit, and then straight home.