Þeir sem vilja bæta framburðinn sinn æfa sig hægt og hlusta vel.

Þeir sem means those who or literally they who.

• þeir = they (masculine plural)
• sem = who/that/which as a relative particle

So Þeir sem vilja... means Those who want...

A useful point: Icelandic often uses masculine plural as the default when talking about people in general or a mixed group. If the group were specifically feminine, you could get þær sem.

Because the subject is plural: þeir = they.

The verb vilja = to want changes by person and number:

• ég vil
• þú vilt
• hann/hún/það vill
• við viljum
• þið viljið
• þeir/þær/þau vilja

So þeir ... vilja is the correct match.

Because it follows vilja.

After vilja (to want), Icelandic normally uses the infinitive of the next verb, just like English:

• vilja bæta = want to improve
• vilja læra = want to learn
• vilja fara = want to go

So vilja bæta framburðinn sinn means want to improve their pronunciation.

Because framburðinn is the direct object of bæta and it is definite.

The basic noun is:

• framburður = pronunciation (nominative singular)

Here, though, the sentence means improve the pronunciation / their pronunciation, so the noun appears in the accusative definite form:

• framburðinn

Very roughly:

• framburður = pronunciation
• framburð = pronunciation (accusative, indefinite)
• framburðinn = the pronunciation (accusative, definite)

Sinn is a reflexive possessive word. It means his/her/its/their own, depending on context.

Here it refers back to the subject Þeir sem vilja..., so:

• framburðinn sinn = their own pronunciation

This is different from a non-reflexive possessive like þeirra, which would more likely suggest someone else’s pronunciation, not the subject’s own.

A key rule:

• use sinn/sín/sitt when the possessor is the same as the subject of the clause

Because that is a normal Icelandic way to express possession.

Icelandic often uses:

• the noun with the definite article
• plus a possessive

So forms like these are perfectly normal:

• bókin mín = my book
• húsið þeirra = their house
• framburðinn sinn = their own pronunciation

To an English speaker it can feel like the pronunciation their-own, but in Icelandic this is standard grammar.

Æfa sig means to practise.

Literally, sig is a reflexive pronoun, so the phrase is something like train oneself or practise oneself, but in natural English we simply say practise.

• æfa = train / practise
• sig = oneself / himself / herself / themselves depending on the subject

Because the subject here is plural (þeir), sig refers back to them:

• Þeir ... æfa sig = They practise

This is one of those verb patterns you just learn as a unit:

• æfa sig

Because hægt is an adverb here, not an adjective.

It describes how they practise:

• æfa sig hægt = practise slowly

Compare:

• hægur = slow (adjective, used with nouns)
• hægt = slowly (adverb, used with verbs)

So:

• hægur maður = a slow man
• hann talar hægt = he speaks slowly

Because vel is the adverb meaning well, and it modifies the verb hlusta (listen).

• góður = good (adjective)
• vel = well (adverb)

So:

• góður hlustandi = a good listener
• hlusta vel = listen well / listen carefully

English often says listen carefully, while Icelandic very naturally says hlusta vel.

Yes. The sentence has two coordinated actions:

• æfa sig hægt = practise slowly
• og hlusta vel = and listen carefully

So the subject Þeir sem vilja bæta framburðinn sinn does both actions.

This is very similar to English:

• Those who want to improve their pronunciation practise slowly and listen carefully.

The structure is:

• Þeir sem vilja bæta framburðinn sinn = the full subject, Those who want to improve their pronunciation
• æfa sig hægt og hlusta vel = the predicate, practise slowly and listen carefully

So the sentence is built like this:

[Subject] + [Verb phrase]

More literally:

• Those who want to improve their pronunciation
  practise slowly and listen well

The relative clause sem vilja bæta framburðinn sinn is attached to þeir and tells you which they/those you mean.

A rough learner-friendly guide:

• Þeir ≈ thayr
  
  • Þ is like th in thin
• sem ≈ sem
• vilja ≈ VIL-ya
• bæta ≈ BYE-ta
• framburðinn ≈ FRAM-bur-thin
• sinn ≈ sin
• æfa sig ≈ EYE-va sig
• hægt ≈ something like hyehkt
  
  • the g is not pronounced like English g
• hlusta ≈ HLUS-ta
• vel ≈ veh-l

A few special notes:

• æ often sounds like eye
• ð is like th in this (though pronunciation can vary by position)
• hl at the start of a word is a special Icelandic sound; learners often approximate it with a plain l at first

A natural rhythm for the whole sentence is:

Þeir sem vilja bæta framburðinn sinn | æfa sig hægt og hlusta vel.