Þvotturinn er enn blautur, svo ég set hann í þurrkarann aftur.

Þvotturinn means the laundry or the washing.

The base noun is þvottur, which is a masculine noun meaning laundry / washing.
The ending -inn is the attached definite article, so:

• þvottur = laundry / washing
• þvotturinn = the laundry

This is very common in Icelandic: instead of a separate word like English the, Icelandic often adds the definite article onto the end of the noun.

Icelandic often uses þvottur as a singular collective noun, much like English can say the laundry.

So even if it refers to several items of clothing, the grammar is singular:

• Þvotturinn er blautur = The laundry is wet

That is why the sentence later uses the singular pronoun hann.

Because adjectives in Icelandic must agree with the noun they describe in gender, number, and case.

Here, þvotturinn is:

• masculine
• singular
• nominative

So the adjective blautur has to match that:

• masculine singular nominative: blautur
• feminine singular nominative: blaut
• neuter singular nominative: blautt

So:

• Þvotturinn er blautur = correct
  because þvotturinn is masculine singular nominative.

Here enn means still.

So:

• Þvotturinn er enn blautur = The laundry is still wet

In other contexts, enn can also mean yet, depending on the sentence, but in this example still is the natural translation.

Here svo means so or therefore.

It connects the two parts:

• Þvotturinn er enn blautur = The laundry is still wet
• svo ég set hann í þurrkarann aftur = so I put it in the dryer again

So svo is functioning like a result word: because that is the situation, this is what I do.

Because setja is the infinitive, meaning to put / to place.

After ég you need the conjugated verb, not the infinitive. The present tense of setja goes like this:

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

So:

• ég set hann í þurrkarann = I put it in the dryer

not ég setja, which would be like saying I to put.

Because hann agrees with the grammatical gender of þvottur, which is masculine.

In Icelandic, pronouns often follow grammatical gender, not natural gender. Since þvottur is masculine, the pronoun referring back to it is hann:

• þvotturinn = masculine noun
• hann = it/he for a masculine noun

In English we would say it, but Icelandic uses the masculine pronoun because the noun is masculine.

Because í can take different cases depending on whether you are talking about movement or location.

• accusative after í = movement into
• dative after í = being in

Here, the laundry is being moved into the dryer:

• ég set hann í þurrkarann = I put it into the dryer

If you were just describing where it is, you would use dative:

• hann er í þurrkaranum = it is in the dryer

So this is a very important Icelandic pattern.

The base form is þurrkari, which means dryer or tumble dryer.

In the sentence, þurrkarann is:

• singular
• definite
• accusative

because it comes after í with movement.

So the forms are:

• þurrkari = a dryer
• þurrkarinn = the dryer
• þurrkarann = the dryer (accusative form)

Aftur means again, and placing it at the end is very natural here:

• ég set hann í þurrkarann aftur = I put it in the dryer again

Icelandic adverb placement can be somewhat flexible, but this word order sounds normal and clear. The final aftur neatly tells you that the whole action is being repeated.

Yes, it is very normal.

The basic order here is:

• ég = subject
• set = verb
• hann = object
• í þurrkarann = direction/place phrase
• aftur = adverb

So the structure is roughly:

subject + verb + object + phrase + adverb

That is a very common Icelandic sentence pattern.

A few useful pronunciation notes:

• Þ in Þvotturinn sounds like th in thin
• ð does not appear in this sentence, but it often sounds like th in this
• ll is not in this sentence either, but many learners watch for it because it often has a special pronunciation
• au in blautur is pronounced roughly like oi in some dialects of English
• þurrkarann has a rolled or tapped r, as Icelandic r usually does

A rough learner-friendly approximation might be:

• Þvotturinn er enn blautur ≈ THVOT-tur-inn er en BLOY-tur
• svo ég set hann í þurrkarann aftur ≈ svo yeh set han ee THUR-ka-ran AHF-tur

These are only approximations, but they can help at first.

Yes, absolutely.

A few natural English translations are:

• The laundry is still wet, so I put it in the dryer again.
• The washing is still wet, so I put it back in the dryer.
• The clothes are still wet, so I put them in the dryer again.

The Icelandic sentence is singular because of þvotturinn, but English may choose either a singular collective noun like laundry/washing or a plural expression like the clothes, depending on what sounds most natural.