Learn Hardcore Icelandic: Hún skráir sig með kennitölu og símanúmeri. - She registers with an ID number and a phone number.

Because skrá sig is the reflexive construction meaning “to sign up/register oneself.” Without sig, skrá means “to register (something/someone else).” So:

Hún skráir sig = She registers herself (signs up).
Hún skráir barnið = She registers the child. Dropping sig in your sentence would change the meaning or make it incomplete.

Why is it sig and not hana?

Sig is the 3rd‑person reflexive object pronoun; it refers back to the subject of the clause (here, hún). Hana means “her” (some other woman), not the subject herself.

Hún skráir sig = She registers herself.
Hún skráir hana = She registers her (another woman).

What case is sig in, and what happens in other persons?

Sig is accusative reflexive (3rd person). Other persons use the ordinary object pronouns, not sig:

1st sg: Ég skrái mig.
2nd sg: Þú skráir þig.
3rd sg: Hún skráir sig.
1st pl: Við skráum okkur.
2nd pl: Þið skráið ykkur.
3rd pl: Þau skrá sig. Note: Some Icelandic verbs take dative objects; then the 3rd‑person reflexive would be sér (dative). But skrá takes the accusative, so it’s sig.

What case does með take here, and why are kennitölu and símanúmeri in those forms?

Með governs either accusative or dative, depending on meaning. For “with, using/by means of” (instrument), it takes the dative. Hence:

með kennitölu (dative sg of kennitala)
með símanúmeri (dative sg of símanúmer) Contrast:
Accusative (bringing/taking along): Hún fór með barnið.
Dative (being with/using): Hún er með barninu. / Hún skar brauðið með hníf (instrument).

Why does kennitala become kennitölu?

That’s the u‑umlaut (u‑hljóðvarp): an ending with -u triggers a vowel change in the stem, turning a → ö in many words. So:

Nom sg: kennitala
Dat sg: kennitölu This pattern is common: the -u ending in the dative singular causes the vowel shift.

What exactly is símanúmeri? What’s the dictionary form?

Símanúmeri is the dative singular of the neuter noun símanúmer (“phone number”). Key forms:

Nom/Acc sg: símanúmer
Dat sg: símanúmeri
Gen sg: símanúmers
Dat pl: símanúmerum

Where should sig go in the sentence? Is Hún skráir ekki sig OK?

Object pronouns normally come right after the finite verb and before sentential negation/adverbs. So:

Correct: Hún skráir sig ekki.
Sounds wrong/unidiomatic: Hún skráir ekki sig. With other adverbs, the pronoun still stays early: Hún skráir sig strax á vefinn.

How do I make it explicit that it’s her own ID number and phone number?

Use the reflexive possessive sinn/sína/sitt, which agrees with the possessed noun:

Hún skráir sig með sinni kennitölu og sínu símanúmeri. Here sinni = dat sg feminine (for kennitölu), and sínu = dat sg neuter (for símanúmeri). If you use hennar (“her”), it can suggest someone else’s: með hennar kennitölu = with her (another woman’s) ID number.

How would I say she registers someone else instead of herself?

Use a non‑reflexive object:

Hún skráir hana. = She registers her (another woman).
Hún skráir Jón. = She registers Jón. Reflexive vs non‑reflexive is the key difference in meaning.

What’s the verb’s dictionary form and basic conjugation?

Dictionary form: að skrá (sig). Present:

ég skrái, þú skráir, hann/hún/það skráir, við skráum, þið skráið, þeir/þau skrá Past:
ég skráði, þú skráðir, hann/hún/það skráði, við skráðum, þið skráðuð, þeir/þau skráðu Past participle: skráð (e.g., Hún er skráð = She is registered).

Could I say “by” doing something instead of “with” a number?

Yes. Use með því að + infinitive for “by (doing) …”:

Hún skráir sig með því að slá inn kennitöluna og símanúmerið. That explicitly means “by entering” the ID and phone number. Your original with með
- dative expresses the instruments (“using” them).

Why is there no “a/an” before kennitölu and símanúmeri?

Icelandic has no indefinite article. Bare nouns cover “a/an.” If you need “the,” you attach a definite ending:

með kennitölunni (the ID number), með símanúmerinu (the phone number).

Any quick pronunciation tips for tricky letters here?

ú in Hún: long “oo” (as in “food”).
á in skráir: diphthong like “ow” in “cow.”
ð in með: voiced “th” (as in “this”); before a voiceless sound (like the k in kenn-), many speakers devoice it toward “th” in “thing.”
g in sig: a soft, fricative “gh” sound.
ö in kennitölu: like the vowel in English “bird,” but rounded. Stress is on the first syllable of each word: Hún SKRÁ‑ir sig MEÐ KEN‑ni‑tö‑lu og SÍ‑ma‑nú‑me‑ri.

What’s the difference between skrá sig, skrá sig inn, and skrá?

skrá sig: to register/sign up.
skrá sig inn: to log in/sign in.
skrá (non‑reflexive): to register/record something or someone else; to enter data.

Do both nouns after og have to be in the same case?

Yes. Coordination doesn’t change case: both must match what the preposition requires. Since með here takes dative, it’s:

með kennitölu og símanúmeri (both dative). Using mixed or nominative forms (e.g., með kennitölu og símanúmer) would be ungrammatical.