Ef rakvélin virkar ekki, þarf hún að þvo froðuna af sér í handlauginni og reyna aftur seinna.

Because the sentence starts with Ef rakvélin virkar ekki, and that whole if-clause counts as the first element of the sentence. In Icelandic main clauses, the finite verb normally comes in second position, so after that opening clause you get þarf first, then the subject hún.

So the pattern is:

Ef ... , þarf hún ...

If you said the main clause by itself, you would normally say Hún þarf ...

Icelandic does not use do/does the way English does. Instead, it negates the verb directly with ekki.

So:

• virkar = works
• virkar ekki = does not work / doesn't work

This is very normal Icelandic word order: the finite verb comes first, and ekki usually follows it.

The base noun is rakvél, meaning razor or electric shaver. The ending -in is the suffixed definite article, so rakvélin means the razor.

Icelandic usually attaches the to the end of the noun rather than using a separate word.

So:

• rakvél = a razor
• rakvélin = the razor

Yes. Hún can mean she, but it can also mean it when referring to a feminine noun.

That matters because rakvél is grammatically feminine, so a razor can be referred to as hún. But hún can also refer to an actual female person. In a sentence like this, the intended meaning comes from the wider context or the translation already given to you.

So for learners, the important point is:

• Icelandic pronouns follow grammatical gender
• hún is not always a human she

Because the verb þurfa normally takes að + infinitive.

So:

• þarf að þvo = needs to wash
• þarf að reyna = needs to try

This is different from some other Icelandic verbs, especially modal-type verbs like geta, which usually take a bare infinitive without að.

Because Icelandic often leaves out a repeated að when two infinitives are joined by og.

So:

• að þvo ... og reyna ...

is the normal, natural way to say it.

The second infinitive reyna still depends on þarf; the að is understood. Also, the subject of reyna is the same as the subject of þvo.

Because froðuna is the definite direct object of þvo.

The noun is froða = foam. Here it means the foam, so it takes the definite ending. It is also in the form required for a direct object after þvo.

So:

• froða = foam
• froðuna = the foam

A learner does not need to know every declension right away, but the key idea is: þvo takes an object, and here that object is the foam.

Af sér is a reflexive expression. It means off herself / himself / itself, depending on who or what the subject is.

The important point is that sér refers back to the subject of the clause. So if the same person or thing is both:

• the one doing the washing, and
• the one the foam is being washed off,

then Icelandic uses the reflexive pronoun.

Also, af takes the dative, which is why the reflexive form is sér here.

Compare:

• af sér = off herself/himself/itself (same subject)
• af henni = off her/it (some other feminine referent, not reflexive)

Because í can take different cases depending on meaning:

• accusative for motion into
• dative for location in

Here the meaning is location: the washing happens in the sink, not movement into it. So Icelandic uses the dative form:

• í handlauginni = in the sink

Also, handlauginni is the definite form, so it means the sink.

Because seinna is the comparative form of seint (late), and Icelandic uses it as an adverb meaning later.

So:

• seint = late
• seinna = later

In this sentence, aftur seinna means something like again later or later on. It is a very natural way to express try again later in Icelandic.