Ýttu á hnappinn til að opna hurðina.

Ýttu á = “press (on).”

• Ýttu is the 2nd person singular imperative of að ýta (“to push/press”).
• To form it: drop the -a from ýta, add -ttu → ýttu.
• á is the preposition “on,” so ýttu á literally “push on.”

In Icelandic, many actions that English expresses without a preposition require one.

• að ýta á means “to press on.”
• If you drop á, the verb ýta can mean “to lean” or “to shove,” so you need á to specify “on the button.”

hnappinn is the definite singular masculine form of hnappur (“button”) in the accusative case.

• The preposition á here indicates movement onto the button, so it takes accusative.
• The suffix -inn marks both definiteness (“the button”) and the masculine singular.

til að + infinitive is the standard way to express purpose (“in order to”).

• til = “for,” að connects to the infinitive opna (“open”).
• Ýttu á hnappinn til að opna hurðina literally “Press the button in order to open the door.”

Icelandic marks the definite article after the noun as a suffix.

• hurð is a feminine noun (“door”).
• To make it “the door” in the accusative singular (direct object of opna), you add -ina, giving hurðina.

Yes. svo að + subjunctive (opnist) expresses a similar purpose/result.

• Ýttu á hnappinn svo hurðin opnist = “Press the button so that the door opens.”
• til að
  • infinitive is more common in everyday instructions; svo að
    • subjunctive is slightly more formal.

Use the 2nd person plural imperative for að ýta:

• ýta → ýtið (drop -a, add -tið)
• So: Ýtið á hnappinn til að opna hurðina.