Learn Hardcore Icelandic: Við fylgjum áætluninni.

fylgjum is the present indicative form of the verb fylgja, which means to follow. It is
• tense & mood: present indicative
• person & number: first-person plural (“we”).

So fylgjum literally means we follow.

Why is áætluninni in the dative case?

In Icelandic some verbs govern specific cases. fylgja is one of them: it takes its object in the dative. Therefore “the plan” must appear in the dative case, giving áætluninni.

What is the base form of áætluninni, and how do you form its definite dative singular?

The lemma (dictionary form) is áætlun (a feminine noun meaning “plan”). To make it definite dative singular you:

Insert the definite-article suffix -in- after the stem.
Add the dative ending -ni.
Result: áætlun
- in
  - ni → áætluninni.

Could you use an indefinite noun (áætlun) instead of áætluninni, and what would the difference be?

Yes. Saying Við fylgjum áætlun means “We follow a plan” (indefinite). Using áætluninni makes it “the plan,” referring to a specific, known plan.

How do you pronounce áætluninni, especially the letters á, æ, and the double nn?

Approximate pronunciation: OW-ET-lun-in-ni, with stress on ET.
• á sounds like ow in cow
• æ like ey in hey (but slightly shorter)
• u in -lun- like oo in book
• double nn means you hold the n-sound a bit longer than a single n

How flexible is the word order? Can you say Áætluninni fylgjum við instead?

Yes. Icelandic main clauses follow the V2 rule: the finite verb (fylgjum) must be the second element. You can front áætluninni for emphasis:
Áætluninni fylgjum við (We do follow the plan).
That fronting simply shifts focus to the plan.

Could you use fara eftir áætluninni instead of fylgjum áætluninni, and is there any nuance?

Absolutely. fara eftir + dative also means to follow (literally “go after”).
• Við fylgjum áætluninni is more concise (single verb governing dative).
• Við förum eftir áætluninni is a verb + preposition construction.
In everyday speech both are common and largely interchangeable.

Why is Við capitalized at the beginning of the sentence?

Like in English, Icelandic capitalizes the first word of a sentence. við (we) is only capitalized because it starts the sentence; otherwise pronouns are not capitalized in Icelandic.