What the Bible Says About the Headcovering
1 Corinthians 11:2-16 gives us the Biblical basis for the head covering for women.
Now I praise you, brethren, that ye remember me in all things, and keep the ordinances, as I delivered them to you. 3 But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God. 4 Every man praying or prophesying, having his head covered, dishonoreth his head. 5 But every woman that prayeth or prophesieth with her head uncovered dishonoreth her head: for that is even all one as if she were shaven. 6 For if the woman be not covered, let her also be shorn: but if it be a shame for a woman to be shorn or shaven, let her be covered. 7 For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man. 8 For the man is not of the woman; but the woman of the man. 9 Neither was the man created for the woman; but the woman for the man. 10 For this cause ought the woman to have power on her head because of the angels. 11 Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord. 12 For as the woman is of the man, even so is the man also by the woman; but all things of God. 13 Judge in yourselves: is it comely that a woman pray unto God uncovered? 14 Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him? 15 But if a woman have long hair, it is a glory to her: for her hair is given her for a covering. 16 But if any man seem to be contentious, we have no such custom, neither the churches of God.
While this passage has created much controversy, God wants us to take this passage literally. This means that men, when praying or prophesying, should have their heads uncovered. They also should keep their hair short. Women, on the other hand, should cover their heads when praying or prophesying. They should also let their hair grow long. This passage applies to home situations, as well as public worship.
All the articles linked to from this website teach this basic doctrine. There may be small variations in practice, but the basic doctrine is the same.