In Icelandic, the way to show politeness is:
  • Greeting with „sæll“ and „daginn“, and using „takk fyrir“ enough.
  • To switch over to more hypothetical sentences, saying “Could you…” and “Would you…” instead of “Can you…” or “Will you…”
  • Throw in “by any chance”
Now let’s compare some sentences.
This is polite:
  • Get ég fengið hamborgara? = Can I get a hamburger?
This is very polite, because you switch over to using the hypothetical:
  • Gæti ég fengið hamborgara? = Could I get a hamburger?
And we can even add more politeness:
  • Gæti ég nokkuð fengið hamborgara? = Could I by any chance get a hamburger?

This is not very polite:
:Geturðu fært þig?
This is polite:
:Geturðu nokkuð fært þig?
This is very polite:
:Gætirðu nokkuð fært þig?

This is polite:
:Ertu til í að koma á morgun?
This is very polite:
:Værirðu til í að koma á morgun?