Ég set hreinu fötin úr þvottakörfunni í skápinn þegar þau eru alveg þurr.

Setja is the infinitive form, meaning to put.
In the sentence, the verb has to agree with ég (I), so it becomes the 1st person singular present form:

• að setja = to put
• ég set = I put
• þú setur = you put
• hann/hún/það setur = he/she/it puts

So Ég set ... means I put ...

In modern Icelandic, föt usually means clothes and is normally treated as a plural noun.
So:

• föt = clothes
• fötin = the clothes

That is why the sentence uses a plural pronoun later: þau = they.

English learners often expect a singular word like clothing, but Icelandic usually uses föt in the plural for ordinary clothes.

Because the noun is definite: fötin = the clothes.

In Icelandic, when an adjective comes before a definite noun, it usually takes the weak form. So:

• hrein föt = clean clothes
• hreinu fötin = the clean clothes

Here:

• hreinu = weak adjective form of hreinn (clean)
• fötin = the clothes

So hreinu fötin means the clean clothes.

Unlike English, Icelandic usually puts the at the end of the noun as a suffix.

So in this sentence:

• fötin = föt
  • -in = the clothes
• þvottakörfunni = þvottakörfu
  • -nni = the laundry basket
• skápinn = skáp
  • -inn = the closet / the cupboard

So instead of a separate word like English the, Icelandic often attaches it directly to the noun.

The preposition úr means out of / from, and it takes the dative case.

So:

• úr þvottakörfunni = out of the laundry basket / from the laundry basket

That is why you do not see the basic dictionary form þvottakarfa here. After úr, the noun has to be in the dative.

Two things are happening:

1. Case change
   The base form is þvottakarfa (laundry basket), but after úr it must be dative.

2. Sound/vowel change
   In the dative form, the a in karfa changes to ö:
   karfa → körfu

Then the definite article is added:

• þvottakarfa = a laundry basket
• þvottakörfu = to/from a laundry basket (dative)
• þvottakörfunni = to/from the laundry basket (dative definite)

This vowel change is a common Icelandic pattern called u-umlaut.

Because í can take two different cases, depending on meaning:

• accusative = motion into
• dative = location in

Here, the clothes are being moved into the closet, so Icelandic uses the accusative:

• í skápinn = into the closet

Compare:

• Fötin eru í skápnum. = The clothes are in the closet.
  (location, so dative)

This accusative/dative contrast after prepositions is very important in Icelandic.

Because föt is a neuter plural noun, and pronouns in Icelandic must agree with the noun’s gender and number.

So:

• fötin = the clothes (neuter plural)
• þau = they (neuter plural)

Even though clothes are inanimate, Icelandic still uses grammatical gender. So þau does not mean the clothes are somehow treated like people; it is just grammatical agreement.

Because it agrees with þau, which is neuter plural.

After vera (to be), the adjective is a predicate adjective, and it must match the subject:

• það er þurrt = it is dry
  (neuter singular)
• þau eru þurr = they are dry
  (neuter plural)

So in this sentence, þurr is the correct plural form for fötin / þau.

Here þegar means when.

So:

• þegar þau eru alveg þurr = when they are completely dry

Yes, the clause order can change. You can also put the when-clause first:

• Þegar þau eru alveg þurr, set ég hreinu fötin úr þvottakörfunni í skápinn.

Notice that if the subordinate clause comes first, Icelandic usually puts the verb before the subject in the main clause:

• set ég, not ég set

That is a normal Icelandic word-order rule.

Alveg means completely, totally, or sometimes quite, depending on context.

Here it strengthens þurr:

• alveg þurr = completely dry

So the sentence is not just saying the clothes are dry, but that they are fully dry.

Yes. In Icelandic, the present tense is often used for habitual actions or general routines, just as in English:

• Ég set ... þegar þau eru alveg þurr.
  = I put ... when they are completely dry.

This sounds like something the speaker normally does.

Depending on context, it could also refer to a near-future action, but the most natural reading is usually a habit or regular practice.