Covering Body in Muslim Prayer (Salat)

While offering prayers, a man should cover his private parts even if no one is looking at him. As for a woman, she should cover her entire body while offering prayers, including her head and hair. It is not necessary for her to cover that part of her face, which is washed while performing Wudhu, or the hands up to the wrists, (or the upper feet up to the ankles, if there is no stranger).

There are six conditions for the dress used in Salat:

It should be clean.
It should be Mubah, as an obligatory precaution.
It should not be made of the parts of a dead body.
It should not be made from pure silk. (Ruling for men only.)
It should not have any gold objects. (Ruling for men only.)
It should not be made of carcass, whose meat is Harram. If a clothe is made from leather, it should be from an animal whose meat is halal.

Place on which prayer is offered must not be usurped. If a person prays on a usurped property, his prayers are void.
Being stable. The place for prayers should not have such a vigorous movement, which would make normal standing, Ruku or Sajdah impossible. In fact, it should not prevent the body from being at ease.
It should not make body or clothes of a person who wants to offer prayers Najis. If the place where one wishes to pray is Najis, it should not be so wet that its moisture would reach the body or the dress of the person praying except than those kinds of Nejasat which are negligible in Salat.
Men should stand in front of women. Women should stand behind men while praying. It is better that her place of Sajdah placed a little back from where a man stands for Salat. Hence, if a woman stands in front of a man, or in the same line, Salat is void.

Source: Grand Ayatollah Sayyid Ali Al-Sistani