Hún festir myndina betur þegar hún slær varlega á naglann með hamrinum.

Because there are two clauses, each with its own subject:

• Main clause: Hún festir myndina betur = She fastens the picture better
• Subordinate time clause: þegar hún slær ... = when she hits ... In Icelandic, you normally state the subject in each clause rather than “sharing” it the way English sometimes can.

Both are present tense (used here for a general/typical action).

• festa (to fasten): ég festi, þú festir, hún/það/það festir
• slá (to hit/strike): ég slæ, þú slærð, hún slær You can often recognize present tense by these personal endings (like -ir in festir and -ær in slær).

myndina is definite: the picture. Icelandic commonly marks definiteness with a suffix (a “postposed article”).

• mynd = a picture (indefinite)
• myndin = the picture (nominative, definite)
• myndina = the picture (accusative, definite)

Because festa takes a direct object, and direct objects are very often accusative in Icelandic.
So Hún festir myndina literally has:

• Subject (nominative): hún
• Object (accusative): myndina

betur means better and it modifies the verb phrase festir myndina (how she fastens it).
Its placement—after the object here—is very natural in Icelandic:

• Hún festir myndina betur = She fastens the picture better
  You could also see adverbs earlier in some contexts, but this placement is common and neutral.

betur is the comparative of the adverb vel (well):

• vel = well
• betur = better (adverb)
• best = best (adverb)

betri is the comparative of the adjective góður (good) and would describe a noun, not the action:

• betri mynd = a better picture (adjective)
• festir ... betur = fastens ... better (adverb)

þegar introduces a time clause (when). After þegar, Icelandic uses subordinate clause word order, which typically keeps the subject before the verb (unlike main-clause inversion in some cases):

• Main clause: Hún festir ...
• Subordinate clause: þegar hún slær ... (subject hún before verb slær)

With slá (to strike), Icelandic often uses the pattern slá á + object to express “hit/strike (on) something,” especially with tools:

• slá á naglann = strike the nail

So á is part of a very common verb + preposition combination here, not just a random “on.”

naglann is definite accusative singular of nagli (nail).

• nagli = a nail (nominative, indefinite)
• naglinn = the nail (nominative, definite)
• naglann = the nail (accusative, definite)

It’s accusative because it’s the object governed by the verb phrase slá á in this idiomatic use.

með (with) usually takes the dative when it means “with (using)” or “together with.” Here it marks the instrument (what she uses):

• með hamrinum = with the hammer

hamrinum is definite dative singular of hamar (hammer):

• hamar (nom. indef.)
• hamarinn (nom. def.)
• hamrinum (dat. def.)

varlega means gently / carefully and it modifies slær (how she hits).
It’s an adverb formed from the adjective varlegur (careful)—a common pattern where an adverb ends in -lega:

• varlegur (adj.) → varlega (adv.)

A rough guide (varies slightly by region):

• Hún: like hoon (long ú)
• myndina: roughly MINN-di-na (the y is similar to a short “i” sound for many learners)
• slær: roughly slye-r (one syllable; æ like “eye” in many accents) Also note Icelandic r is usually trilled or tapped, not the English approximant.