Learn Hardcore Greek: Σήμερα δεν θέλω να ακούσω τις ειδήσεις, θέλω μόνο να χαλαρώσω στο σαλόνι. - Today I don’t want to listen to the news; I only want to relax in the living room.

Greek verb endings usually show the subject, so θέλω already means I want. You add εγώ only for emphasis or contrast (e.g., Εγώ δεν θέλω… αλλά εσύ θέλεις…).
δεν is the standard negation word used with most verbs in the present/past (non-imperative) forms.

Why is δεν placed before the verb θέλω?

In Greek, δεν typically comes directly before the verb phrase it negates. So δεν θέλω = I don’t want. If you move δεν, you either sound unnatural or you change what is being negated/emphasized.

What exactly does να do in να ακούσω and να χαλαρώσω?

να introduces the subjunctive in Modern Greek. After verbs like θέλω (I want), Greek uses να + verb rather than an infinitive.
So English I want to hear / to relax becomes Greek θέλω να ακούσω / να χαλαρώσω.

Why is it ακούσω (not ακούω)?

ακούσω is the aorist subjunctive (perfective aspect). With θέλω να…, Greek often chooses:

aorist/perfective (να ακούσω) = “to listen/hear (as a complete event / not necessarily ongoing)”
present/imperfective (να ακούω) = “to be listening (ongoing/repeated)”

Here, να ακούσω τις ειδήσεις sounds like “I don’t want to listen to the news (at all / as an act).”

Does ακούσω mean “hear” or “listen”?

ακούω / ακούσω can cover both ideas depending on context. With something like τις ειδήσεις (the news) it usually means listen to (like listening to a broadcast), even though the basic verb is “hear.”

Why is τις ειδήσεις in this form?

οι ειδήσεις = the news (plural, feminine).
Here it’s the direct object of ακούσω, so it goes into the accusative plural:
οι ειδήσεις → τις ειδήσεις.

Why is ειδήσεις plural? In English, “news” is usually singular.

In Greek, η είδηση is a piece of news / an item, and οι ειδήσεις is the normal way to say the news as a category or broadcast. So Greek treats it as plural.

Why is να repeated: δεν θέλω να ακούσω… θέλω μόνο να χαλαρώσω…?

Each verb θέλω introduces its own να-clause, so you repeat να with each desired action:

θέλω να ακούσω…
θέλω να χαλαρώσω… That’s the normal structure in Greek.

What does μόνο modify, and where can it go?

μόνο means only / just. In θέλω μόνο να χαλαρώσω, it limits the intention: “I want only to relax.”
Word order is flexible, but positions change emphasis:

Θέλω μόνο να χαλαρώσω = I only want to relax (not do other things)
Θέλω να χαλαρώσω μόνο can sound like “only relax” (sometimes a bit more marked)

What is στο σαλόνι grammatically?

στο is a contraction of σε + το = in/at the.
σαλόνι is neuter; nominative/accusative το σαλόνι. After σε, it becomes στο σαλόνι = in the living room.

Why is there a comma, and could it be a semicolon?

The comma separates two closely linked clauses:
Σήμερα δεν θέλω… , θέλω μόνο…
A semicolon would also be acceptable in more formal writing, but a comma is very common in everyday Greek for this kind of contrast.

How is this sentence typically pronounced (roughly) for an English speaker?

A rough guide (not IPA):
SÍ-me-ra then THÉ-lo na A-kú-so tis i-DÍ-sis, THÉ-lo MÓ-no na ha-la-RÓ-so sto sa-LÓ-ni.
Notes:

Stress marks show where the emphasis goes: Σή-, θέ-, -κού-, -δή-, μό-, -ρώ-, -λό-.
δεν sounds like then (with a soft th as in this in most contexts).