When are Muslim women supposed to cover their heads?

Women only have to wear the hijab when they have gotten through their 'puberty' process and are considered grown-ups. Before that, it is their choice and they do not have to wear it.

The father, brother(s), uncle(s), grandfather(s), husband and any female can see the woman without any hijab. Cousins and any other stranger male cannot, however, see them without the hijab.

Wearing a hijab doesn't only mean to cover your head but to also wear appropriate clothes in front of stranger males.

answer:

All parts of free women, except their palms and faces, including their wrists, outer parts of their hands, hanging parts of their hair and under their feet are awrat (and therefore they must be covered) during a namâz, according to the Hanafî Madhhab. There are also quite a number of valuable books saying that outer parts of hands are not awrat. According to them, it is permissible for women to perform namâz while outer parts of their hands up to wrists are bare.