búið

In a sentence

• Við erum búin að klára verkefnið.

  We have finished the task.

  Here 'búin' is used as part of a verbal phrase indicating the completion of an action, commonly constructed with a form of the verb 'vera' (to be) and an adjective or past participle.

• Búið var að taka til áður en gestirnir komu.

  The cleaning had been done before the guests arrived.

  'Búið' here functions as a past participle used in an impersonal way to indicate that an action was completed.

• Ég kem þegar ég er búinn að lesa.

  I will come when I have finished reading.

  In this example, 'búinn' is used similarly to the first example but agrees with the subject in gender and number.