Learn Hardcore Icelandic: Hún einbeitir sér í eina klukkustund án símans. - She focuses for an hour without the phone.

Because að einbeita sér “to concentrate” takes the reflexive in the dative case. The dative reflexive for 3rd person is sér. The accusative reflexive is sig, but that’s used with verbs that take the accusative (e.g., Hún meiddi sig “She hurt herself”). With this verb you always say:

ég einbeiti mér
þú einbeitir þér
hún/hann/það einbeitir sér
við einbeitum okkur
þið einbeitið ykkur
þær/þeir/þau einbeita sér

What does í eina klukkustund do here, and why is it accusative (eina)?

It expresses duration: “for one hour.” In Icelandic, duration is very often shown with í + accusative. The numeral einn declines, and because klukkustund is feminine and in the accusative, you get eina:

nominative fem.: ein
accusative fem.: eina So: í eina klukkustund = “for one hour.”

Could I say í einni klukkustund instead?

Not for “for one hour.” Í + dative with time typically means “in/within/during (a given time frame),” not a bare duration. For “within one hour,” Icelandic usually prefers á einni klukkustund (“in one hour, i.e., it took one hour to complete”). Keep:

for a span = í + accusative: í eina klukkustund
within/in the course of (completion time) = often á + dative: á einni klukkustund

Can I drop í and just say Hún einbeitir sér eina klukkustund?

Sometimes bare accusative time expressions are used for duration (e.g., Hann svaf tvo klukkutíma). Here, though, í is very natural and idiomatic: Hún einbeitir sér í eina klukkustund. Without í can sound stilted in this particular sentence; prefer keeping í.

Is í klukkutíma also possible? What’s the difference from í eina klukkustund?

Yes: í klukkutíma = “for an hour,” a bit less specific/less emphatic than “for one full hour.”

í eina klukkustund highlights the exact one-hour span.
í klukkutíma is the common, everyday way to say “for an hour.”
Both are correct here.

Why is it án símans and not án síma?

Because án (“without”) governs the genitive.

án síma = “without a phone” (indefinite)
án símans = “without the phone” (definite, typically “her phone/that phone”)
The noun is sími (m.). Genitive singular is síma (indef.), and with the definite article it becomes símans.

Where does the reflexive pronoun go in the sentence? Could I move it later?

The normal order is Subject – Verb – (short object pronoun) – Adverbials. So Hún einbeitir sér í eina klukkustund án símans is the default. You wouldn’t say “Hún einbeitir í eina klukkustund sér…”. If you front something (for emphasis), the verb must still stay in second position:

Í eina klukkustund einbeitir hún sér án símans.

Do I need to say what she’s concentrating on? How would I add that?

You can leave it implicit, as here. If you want to specify the focus, use að + dative:

Hún einbeitir sér að verkefninu. “She concentrates on the project.”
Hann einbeitir sér að náminu. “He concentrates on his studies.”

How do I conjugate að einbeita sér?

Present:

ég einbeiti mér
þú einbeitir þér
hún/hann/það einbeitir sér
við einbeitum okkur
þið einbeitið ykkur
þær/þeir/þau einbeita sér

Past (preterite):

ég einbeitti mér
þú einbeittir þér
hún/hann/það einbeitti sér
við einbeittum okkur
þið einbeittuð ykkur
þær/þeir/þau einbeittu sér

Imperative:

(þú) einbeittu þér!

Can the reflexive sér refer to someone other than the subject?

No. Reflexive pronouns in Icelandic always refer back to the subject of the clause. In third person, sér/sig can only mean “herself/himself/themselves” (i.e., the subject). To refer to another person, you’d use a non‑reflexive pronoun (e.g., henni), but note that with this verb the idiom is specifically einbeita sér (að…), so you don’t replace sér with a different person pronoun.

Are there synonyms for að einbeita sér?

að einblína á + accusative: “to fixate/focus on.” Example: Hún einblínir á verkefnið.
að hafa huga við: “to pay attention to.”
Use patterns correctly: einbeita sér að + dative, but einblína á + accusative.

How do I pronounce the tricky parts?

Approximate guide:

Hún ≈ “hoon” (long oo)
einbeitir ≈ “EIN-pay-tir” (EIN as in English “vein,” tir like “tir”)
sér ≈ “syair” (sj- like “sy” + long air)
í ≈ “ee” (long)
eina ≈ “AY-na”
klukkustund ≈ “KLUHK-kuh-stoond” (u like German “ü”; kk is hard, with a slight h-sound)
án ≈ “own” (like English “own,” one syllable)
símans ≈ “SEE-mans” (long ee in the first syllable)

Put together: roughly “Hoon EIN-pay-tir syair ee AY-na KLUHK-kuh-stoond own SEE-mans.”