How can one grieve the death of a beloved person in a way that is consistent with the Quran and Sunnah?

Grieving for the deceased is a natural matter and there is no sin in it, as is weeping without wailing. The eye sheds tears and the heart grieves, and this does not contradict contentment with divine decree; rather, it is a mercy. What is blameworthy is lamenting, wailing, and similar vain speech.